Motion Second Lawof Motion

188 Newton's Laws of

Formulafor true
force is IMP PMT 294,
1.
(b) F mdv
Multiple Choice Questions (a) F ma d

dmv (d) F= md'x

(c) F= dt d2
First law of motion
A. Another
string C
A metre
scale is
moving with uniforn velocity. This i
1 A mass of 1 kg is suspended by a string If a sudden jerk is 2.
IS Connected to its lower
end (see figure),
A (a) The force acting on the scale is zero, but atorq
[NCERT Ex
given to C, then
(a) The portion AB of the string will break can act on the scalo
the centre of mass
(b) The portion BC of the string will break (b) The force acting on the Scale iS zero arnd the
(c) None of the strings will break acting about centre of mass of the Scale is aso en
(d) The mass wll start rotating
constant speed along a straight actíng on it need not be
2. A particle is moving with a [AFMC 2001] (c) The total force
line path. Aforce is not required to torque on it is zero
(a) Increase its speed nor the torque need to be zero
(d) Neither the force
(b) Decrease the momentum
(c) Change the direction 3. Ifa bullet of mass 5 gm moving with velocity 10
penetrates the wooden block upto 6 cm. Then the
(d) Keep it moving with uniform velocity MP PVT
3. When a bus suddenly takes a turn, the
passengers are force imposed by the bullet on the block is
1999; CPMT 2000, 01] (b) 417N
thrown outwards because of [AFMC (a) 8300 N
(a) Inertia of direction (b) Acceleration of motion (d) Zero
(d) Both (b) and (c) (c) 830 N
(c) Speed of motion t=0 wia
4 A person sitting in an open car
moving at constant velocity 4 A body of mass 0.4 kg starting at origin at
subiecz
throws a ball vertically up into air. The ball falls of 10m/s in the positive x-axis direction is
2004]
(EAMCET (Med.) 1995; MH CET 2003; BCECE
constant force F =8N towards negative x-axis. Caloiz
(a) Outside the car 2m
(b) In the car ahead of the person position of the partide after 25 seconds [AMU (Ena.)
(c) In the car to the side of the person (a) 6000 m (b) -8000m
(d) Exactiy in the hand which threw it up (c) +4000 m (d) +7000 m
5 A car is moving with unifom velocity on arough horizontal
road. Therefore, according to Newton's first law of motion 5 A particle moves in the xy-plane under the action i a
momentum p
(a) No force is being applied by its engine F Such that the components of its linear
(b) A force is surely being applied by its engine time tare p, = 2 cost. p. = 2sin t. The ange be
(c) An acceleration is being produced in the car and p at time t is [MP PET 1996; UPSEAT
(d) The kínetic energy of the car is increasing
(a) 90 (b) 0°
6 Aperson is sitting in a travelling train and facing the engine.
He tosses up a coinand the coin falls behind him. It can be (c) 180° (d) 30°
concluded that the train is (SCRA 1994] 6 Abody of mass 5kg is suspended by aspring balane
(a) Moving forward and gaining speed
(b) Moving forward and losing speed
inclined plane as shown in fiqure. The sprts
measure
(c) Moving forward with uniform speed
(a) 50 N
(d) Moving backward with uniform speed
Aball is traveling with uniform translatory motion. This (b) 25 N
7.
means that [NCERT Exemplar] (c) 500 N 30
(a) It is at rest
(b) The path can be astraight line or circular and the ball
(d) 10 N
7 mases3
travels with uniform speed Same íorce acts on two bodies of different
5 kg required o 2
(c) Al parts of the ball have the sarne velocity (magnitude
and direction)and the velocity is constant
initially at rest. The ratio of times KeralaPNT
sarme final velocity is
(d) The centre of the ball moves with constant velocity and (a) 5:3
the ballspins about its centre uniformly (b) 25:9
(c) 9:25
(d) 3:5
 189
Newton's Laws of Motion
A particle of mass 0.3 kg is with a velocity of
subjected to a force F=kk An army vehicle of mass 1000 kg is rnoving
8
15.
with k= 15 N/m. What will be its initial of 1000 N due
acceleration if it is 10m/s and is acted upon by a forward force
released from a point 20 cm away from the origin retarding force of 500 N due to friction.
to the engine and a
(Pb. PMT 2000]
[AIEEE 2005; BCECE 2006) What will be its velocity after 10s
(a) 5 m/s? (a) 5 m/s (b) 10 m/s
(b) 10 m/s
(c) 3 m/s? (c) 15 m/s (d) 20 rnls
(d) 15 m/s A vessel containing water is gjven a constant acceleration a
16.
9 A ship of mass 3x10' kg initially at rest is
pulled by a force towards the right, alonga straight horworntal path. Which of the
of 5x10 N through a distance of 3 m.
Assume that the following diagam represents the surface of the liquid (IT 1981l]
resistance due to water is negligible, the speed of the ship is
(IT 1980; MP PMT 2000)
(a) 1.5 m/s (b) 60 m/s
(c) 0.1 m/s (d) 5 m/s
(A) (B) (C) (D)
10 The linear momentum p of a body moving in one (a) A (b) B
dimension varies with time according to the equation
(c) C (d) D
p =a+ bt 2 where a and b are positive
constants. The net 17. A closed compartment containing gas is rnoving with sorne
force acting on the body is [MP PMT 1993; Pb. PET 2002) acceleration in horizontal direction. Neglect effect of gravity.
(a) Aconstant (b) Proportional to t? Then the pressure in the compartrnent is (IIT-JEE 1999]
(c) Inversely proportional to t (d) Proportional to t (a) Same everywhere (b) Lower in front side
(c) Lower in rear side (d) Lower in upperside
11. The adjacent figure is the part of a horizontally stretched net.
section AB is stretched with a force of 10 N. The tensions in
18. A player caught a cricket ball of mass 150 grn moving at the
rate of 20 m/sec. If the catching process be cormpleted in 0.1
the sections BC and BF are [KCET 2005] sec the force of the blow exerted by the ball on the hands of
player is (AFMC 1993; CBSE PMT 2001;
150° 150°
BHU2001; Kerala PET 2005; AIEEE 2006]
(a) 0.3 N (b) 30 N
(c) 300 N (d) 3000 N
120°
(a) 10 N, 11 N 19. A body of mass 5 kg starts from the origin with an
H initial
(b) 10N, 6N velocity u=30i +40jms.If a constant force F =í+5j)N
120° 120°
(c) 10N, 10 N acts on the body, the time in which the
A y-component of the
(d) Can't calculate due to insufficient data velocity becomes zero is (EAMCET (Med.) 2000]
(a) 5 seconds (b) 20 seconds
12.
A force vector applied on a mass is represented as (c) 40 seconds (d) 80seconds
F =6i -8j +10k and accelerates with lm/s. What will 20. A block of mass 5kg is moving
horizontally at a speed of
be the mass of the body 1.5 m/s. A perpendicular force of 5N acts on it for 4
sec.
(CBSE PMT 1996, 2009; Odisha JEE 2011] What will be the distance of the block from the point
the force started acting where
(a) 10/2 kg (b) 2/10 kg (Pb. PMT 2002]
(a) 10 m (b) 8 m
(c) 10 kg (d) 20 kg (c) 6 m (d) 2 m
3. Acricket ball of mass 250 gcollides with abat with velocity 21. Which one of the following is not a contact force
10 m/s and returns with the same velocity within 0.01 (Kerala PET 2010]
second. The force acted on bat is [CPMT 1997] (a) Viscous force (b) Air resistance
(a) 25 N (b) 50 N (c) Friction (d) Buoyant force
(e) Magnetic force
(c) 250 N (d) 500 N
22. A body with mass 5k is acted upon by a force
14. Apendulum bob of mass 50 gm is suspended from the
Ceiling of an elevator. The tension in the string if the elevator F=(-3i +4) N. If its initial velocity at t=0 is
goes up with uniform velocity is approximately V=(6i -12i)) ms , the time at which it will
[AMU(Med.) 1999) just have a
velocity along the Y-axis is (NCERT Exemplar)
la) 0.30N (b) 0.40N (a) Never (b) 10s
(c) 0.42 N (d) 0.50N (c) 2s (d) 15s
 balance and a
with aspring body
190 Newton's Laws of Motion
and ocquires a
velocity
30. Ila person
goes up and up in an aeroplane, then the reading d
weight ofthebodyasindicated by the spring balance
ha ngjng
hom
the car
two s'onds, Assming IAIIMS 1998; JIPMER
algcast, Vi 0) in exerted on the
unitom aceleration, the toco
|NCERT Exemplar) increasing
Oves with
(a) Go on
decreasing
and is eNetod by the
carengine (b) Go on decrease
castwant increase and then
tyres (c) First
the fiction on the the same
(b) castwand and is due to (d) Remain
dropped from a
400 gm is
eNerted by the rod 31. Aball of mass
ground hits the ball vertically upwards
to the engine and boy onthe
(c) Moe than eastward exerted due average force of
100 newton so that
with an
Overomes the fiction of the
road 20 m. The time for which the ball er
vertical height of
10m/s1
(d) exerted by the engine in contact with the bat is [g = [MP PMT 1A
suddenly turns (b) 0.08s
hockev plaver is moving northward and opponent. The (a) 0.12s
24. A an
speed toavoid (NCERT (d) 12 s
westward with the same Exemplar] (c) 0.04s
force that acts on the player is ballls each of mass m
impinge elastically each se
along westward nsmall
(a) Frictional force 32.
velocity u. The force
experiencedh.
(b) Muscle force along
southward on asurface with
[MP PMTPET I
along south-west surface will be
(c) Frictional force
south-west RPET 2001; BHU2001; MP PMT
(d) Muscle force along according to the law
A body of mas 2kg travels (b) 2 mnu
25. where, q=4ms
,p=3mns1 and (a) mnu
1
x(t) = pt + qt +rt (d) -mnu
force acting on the body
at t = 2s is (c) 4 mnu 2
r=5ms The (NCERT Exemplar)
same height d
kgis connected at the
(b) 134N 33. A rope of mass 0.1 Own wagt
(a) 136N allowed to hang under its
(d) 68 N opposite walls. It is the wall, the 1
(c) 158N contact point between the rope and
upwards by the
mass 0.2 kg is thrown vertically 0.2m while The ES
with respect tohorizontal.
26. A ball of
hand. If the hand
moves makes an angle =10° [DUMET
applying a force by upto 2m height further, midpoint between the wall is
ball goes rope at its
applying the force and the = 10nm/s2
in the
(b) 2.56N
the force. Consider g (a) 2.78N
find the magnitude of [AIEEE 20061
(d) 2.71N
(b) 20N (c) 2.82 N
(a) 16 N Smooth wede
(d) 4N a
A block of mass m is placed on
(c) 22 N
a constant force.
34. acceleratedhhorie
A body of mass 4 kg
is accelerated upon by a distance of inclination . The whole system 0s wedge.The
27. the first second and ho

travels a distance of 5 m in acting on the body is So that the block does not slip on acceleration
second. The force
2m in the third (KCET 2008] the block (gis(CBSEPMTAN
exerted by the wedge on
(b) 8N gravity) will be
(a) 6
(d) 4N (b) mgsin
(c) 2N held in air horizontally bu (a) mgcos
M is just
ASolid disc of mass vertically upwards to strike the
(d) malcos wt
28.
throwing 40 stones per sec each stone
(c) mg down

6 ms.If the mass of descending

disc each with avelocity
sho
(g = 10ms 2) 35 A balloon with mass m is mass
the mass of the disc How much
is 0.05ka what is (Kerala (Engg.) 2001] acceleration a(where a < g). moving
starts lCBSEPMT
(b) 0.5kg removed from it so that it
(a) 1.2kg acceleration a
(d) 3kg
(c) 20kg bu
target, its velocity decreasps
ma

a bullet is fired at a
ma
additional thickness (a) (b)
30cm into it. The
When q -a
29.
balf after penetrating coming to rest is (Kerala PMT 2007]
g+a
before
will penetrate (b) 40 cm 2ma
2ma (d) g-a
(a) 30 cm (d) 50 cm (c)
g+a
(c) 10 cm
 ÎNed hictionless
inclined planes making an
'withthe vertical angle 30°
placed on the
are shown in the
figure. Two 40. Newton's Laws of Motion 191
Aand Bare two planes.
halacceleration of A with respect to B What is the
blocks The mass of a
lift is
[AIEEE relative Supporting cable is 280002000N. kg. When the tension in the
20101 (CBSE
then its
acceleration is
PMT 2009: Similar
B (a) 30 ms Manipal MEE 1995)
(c) 4 ns downwards (b) 4 ms upwards
60%
41,
Three weightsdownwards
W. 2W and
(d) 14 ms 2 upwards
R0 3W
a 49 ms in vertical direction springs suspended
of the rod and from a rigid
are connected to
identical
A 49ms in horizontal direction the weiahts fall horizontal
rod. The
assembly
weights from the rod are such freely. The positions
of the
98 ms in vertical direction (a) 3W will be that (Roorkee 1999]
d Zero (b) W farthest
will be farthest
naticles of mass m each are (c)
ins af length 2a. The tied at the ends of a All will be at
the same
whole system is kept on a light (d) 2W will be distance
onzontal surtace with the string
d ticht so that each mass is at
frictionless 42. A10 kg stone isfarthest
adistance 'a from the 30 kg wt. The suspendedwith a rope of
breaking strength
raised through aminimum
center P time in which the
s shoun in the stone can be
g=10N/ kg ) height 10 m starting from rest is (taking
figure). Now,
he mid-point of the
led vertically upwardsstring a
m
is
(a) 0.5 seconds [AMUPMT 2009]
Smallbut constant force F.with (b) 1.0seconds
As a
resut, the particles
move
a
(c) 2V3 seconds
The magnitude of towards each other on the (d) 2.0 seconds
RNeen them becomesacceleration, when the surface. 43. A person of
2x, is separation
[IIT-JEE 2007)
mass 60 ka is
inside a lift of mass 940 ka
presses the button one control
a F and
F upwards with an acceleration panel. The lift starts
1.0m/s. If q = 10 msmoving
Zm a-) (b) X

2m Ja-x tension in the supporting the

F x
(a) 1200N cable is (CBSE PMT (Pre.) 2011]
2m a (d) F Va- y2 (b) 8600 N
Asolud 2m (c) 9680 N
n thesphere mass 2kg is resting
of
X
44. Alift is going up.
(d) 11000 N
The total mass of the lift
figure. The cube is inside a cube as shown is 1500 kg. The and the
=5ti +2t moving with a velocity in passenger
the graph. Thevariation the speed of the lift is as given in
SmOoth. j)mls.
Here t is
e the time in second. All surface t = 11th sec will tension in the m/secrope
speed
in
pulling the lift at
hat is The sphere is at
be
rest with
Taxe g=the10total force exerted by the sphere
respect to the cube. (a) 17400 N 36
mls) on the cube. (b) 14700 N
(c) 12000 N
b 29N
A B (d) Zero

A89 N
45. A person is
standing in an elevator. In which 10 12
D
finds his weight less than actual
weight situation he
lat
late
(a) The elevator
moves upward with constant (AIIMS 2005)
igntal el of moveswaternormally
of
with
a speed v1 towards a
(b) The elevator
acceleration
moves
downward
acceleration
with
constant
eed of vz. water at the uniform area of cross-section. The
rate of volume Vper second at a lc) The elevator
moves upward with uniform
)ashes adongThe density
the
of water is p. Assume that water (d) The elevator moves velocity
downward with uniform yelocihy
motion. jetThesurfacemagnitude
of the
plate at right angles to the
of the force acting on the
46. Asphere is accelerated upwards by a
strenath is four times its weight. The cord whose braking
the of
water is [IIT 1995) with which the sphere can maximum acceleration
move up without breaking the
(b) V luItvz) Cord is

(d)
(a) g (b) 3q (RPMT 2005)
(c) 2g (d) 4g
 19 Newton's Laws of Notton
51.
instant he finds, swale vading has

What should we ncude

thon cmes back hanged front
onstnt
The itt ws
motion upwands
The litt wns in nstant notion
(c) The litt while in constant motion
suddenlv
dowmwans
upwands
48 while
() The lift in constant
suddenly stopped motion doww
55. The time period of a simple pendulum
stationarv lift is found to be T, If the ift
upwands with an acceleration g3, the time starts
measuredaccaits
(CRSE MT 199S) (EAMCET 1994; CMEET Bihar 1995; period
RP
(a) TV3 (b) TV3/2
(d) 21 (c) T/Ns (d) T/3
49 R n a s t a n At, a man is stadiN with a chet full ot 56. Alift acoelerated downward with acceleration
Wat. havig a ole at is m. The rate of ow of water the lift throws a ball upward with 'd. Ana
thrgh this ho is R li the it stats to me p and down acceleration
Then acoeleration of ball observed by observer m
with sae eraton a then that rats of low of water earth, is
ar R. ad R then (UPSEAT 2008) (a) (a+ ) upward [AIEEE 2
(b) (a- a) upward
(b) A R>R (c) (a+ qo) downward (d) (a- a,) downwart
A neference frame attached to the earth
(d) R, R>R 57. [AFMC 2
(a) Is an inertial frame by definition
50. A mone of mas 20 is holding avertial rope. The rope
wll not break when a mass of 25 kg is suspended from it but (b) Cannot be an inertial frame because earth is EOØ
round the sun
wl break if the mas exis 25 Âg. What is the maximum (c) Is an inertial frame because Newton's laws are arnica
aoeleration with which the monkey can cdimb up along the (d) Is an inertial frame because the earth is rotating a
roe g=10 ms) [CBSE PMT 200S) its own axis
(a) 10 ms (b) 25 ms 58. For ondinary temestrial experiments, the obsen s
(c) 25 ms (d) 5 nms inertial frame in the following cases is (KCET2

A sring balanoe is attached to the ceiling of a lft. A man (a) A child revolving in a giant wheel
51.
(b) A driver in a sports car moving with a consa
hangs his bag on the spring and the spring reads 49 N. speed of 200 kmh' on a straight rod
when the ift is stationarv. if the lift moves downward with (c) The pilot of an aeroplane which is taking ofi
an acceleration of 5m/s. the reading of the spring balance (d) A vclist negotiating a sharp curve
will be [AIEEE 2003: Similar SCRA 1994; RPET 2003: 59. A body of mass 0.05 kg is observed to a at
Kerala PMT 2003; RPMT 2005] acceleration of 9.5 ms 2 The opposing force of air
[KCET
(a) 49N (b) 24 N body is (g =9.8s)
(d) 15 N (a) 0.015 N (b) 0.15N
(c) 74N
(c) 0.030 N (d) Zero
tne t=l
52. A lift of mass 1000 kg is moving with an acceleration of lms 60. A partide of mass mis at rest at the ongn at
in upward direction. Tension developed in the string. which is subjected to a foroe F(t) = Fein the x (AIEEE
directin
connected to the lift is (g=9.8 ms) (CBSE PMT 2002;
DCE2009: Similar NCERT 1977: Manipal MEE 1995: v(t) is depicted by which of the following cunes
Kurukshetra CEE 1996; MP PMT 1999, 2000)
(a) 9,800 N (b) 10.000 N (a) (b)
(d) 11,000 N mb
(c) 10,800 N
acceleration a. A man in the be
53. Alift is moving down with
the ball as
drops a ball inside the lift. The acceleration of
standino
observed by the man tn the lift and a man
respectively (AIEEE 2002)
stationary on the ground are (c) mb (d) mb
(b) g-0.g -a
(a) g.g
(d) a,g
(c) g -a.g
 Newton's Laws of Motion 193
variation of
momentum with time of one of the body in
5.
The collision is shown in fig. The instantaneous force Abird weighs 2 kg and is inside a closed cage of 1 Kg
conrespondingto point Sarts iying, then what is the weight of the bird and cage
[AFMC 1997]
maNimum assembly
(a) 1.5 kg (b) 2.5 kg
(alP
(c) 3 kg (d) 4 kg
R 6.
R
A man is standing at a spring platform. Reading of spring
P balance is 60 kg wt, If man iumps outside platform, then
reading of spring balance
person used force (F), shown in figure to move a load [AFMC 1996; AIIMS 2000: Pb. PET 2000]
t velocity on given surface
A (a)
(AIIMS 2006) First increases then decreases to zero
withconstant
(b) Decreases
(c) Increases
(d) Remains same
7 When a horse pulls a wagon, the force that causes the horse
profile to move forward is the force (Pb. PET 2004]
Hentfy the conect surface (a) The ground exerts on it (b) It exerts on the ground
(c) The wagon exerts on it (d) It exerts on the wagon
(b)
8 A bird is sitting in a large closed cage which is placed on a
spring balance. It records a weight of 25 N. The bird (mass
m =0.5 kg) flies upward in the cage with an acceleration of
2m/s.The spring balance willnow record a weight of
(d) [MP PMT 1999]
(a) 24 N (b) 25 N
Aconstant force acts on a body of mass 0.9 kg at rest for (c) 26 N (d) 27 N
Is. I the body moves a distance of 250 m, the magnitude 9. A light spring balance hangs from the hook of the other light
dt the force is (EAMCET (Engg.) 2000] spring balance and a block of mass M kg hangs from the
lal 3N (b) 3.5N fomer one. Then the true statement about the scale reading is
lc 4.0N [AIEEE 2003]
(d) 4.5N (a) Both the scales read M/2 kg each
(b) Both the scales read M kg each
Third Law of Motion (c) The scale of the lower one reads M kg and of the upper
Swmming is possible on account of [AFMC 1998, 2003] one zero

la) First law of (d) The reading of the two scales can be anything but the
motion (b) Second law of motion sum of the reading will be M kg
d Third law of
motion (d) Newton's law of gravitation 10. Abook is lyingon the table. What is the angle between the
Sandis
kgs. Thebeing dropped on a conveyor
force necessary to keep the
belt at the rate of M action of the book on thetable and the reaction of the table
on the book [Kerala PMT 2005)
belt moving with a
Onstant velocityof um/s will [CBSE PMT 2008] (a) 0° (b) 30°
be
Mu (c) 45° (d) 180°
2 newton (b) Zero 11. The tension in the spring is [AMU(Engg.) 2001)
d Mu newton 5N O0000005
ATman is (d) 2 MuNewton (a) Zero (b) 2.5N
Ho
can
la By y
he get standing
himself to the
at the
centre of frictionless pond of ice.
shore [J & KCET 2005] (c) 5N (d) 10 N

b) By throwing
his shirt in vertically upward direction 12. Ten one-rupee coins are put on top of each other on a table
Each coin has a mass m. which of the following statements
spiting
c) He
horizontal y
d wil wait for the ice to melt in pond
is not true [AMUPMT 2009)
(a) The force on the 6h coins (counted from the bottom)
Unable
to get at the shore due to all the coins on its top is equal to 4 mg
(downwards)
la
The propulsion is associated with [J & KCET 2010) (b) The force on 6n coin due to 7h coin is 4ma
b
The Conservation of angular momentum (downwards)
)
The Conservation mechanical
of mass (c) The reaction of the 6th coin on the 7h coin is 4mng
Conservlawationof motion energy
of (upwards)
(d) The total force on the 10h coin is 9 mg (downwards)
 Matlon
94 Newnn's i aw# of

00, t i e

mpaloo
Coneervalon of Linear Moentumand
inparled on itin Ho) is
(b) 20

(e) 0
() 000 /
D0m When hit by afoe, whih a1s n atat/
ed ofihe ahell le ti0 wa, callalo ihe recoll opoed impulsive fore is
mmte |AMO (En) 2012| (b) 01Ns
(a) 0.5 M6 17
(b) Hm/ (c) 03N6 (d) 12Ns
(a)
The figure shows the positioD- ime t)ga 4
() den/ () lom/n
mual have conslanl
dimensional motion of a body o mass 04i
A lody, wheae monentun lo conalat, magnitude of each impulse is
|AIMS 20001

(a) force (b) Velocily

() Aceleralon ( ) Al ol ihese
Abody of mass m 3613ky lo movg along ihe xaxle witlh
1
momentum i6 10 12 14 16
a apeed of b00 ms The magnllude of ils
rocordedl as |AEEE 2008) I(6)

(a) 17.5oh kg ms (b) 1756 ky ma! (a) 0:2 Ns (b) 04Ns

(e) 17.57 ky ma (d) 17.6ky ms (e) 0.8Ns (d) 16Ns
Newson's second and thid laws of moton lend to the 12, A cricket ball of mass 1504 has an inita
conservation of (Kerala PMT 2009] 10
u-(3i +4)ms and a final velocity
(a) Linear momentum (b) Angular Momentum moec
(d) Kinetic energy aller being hit, The change in momentum (final
(e) Potential energv (NCEKTE
- initlal nomenturm) is (in kgrns )
(e) Force
(a) Zero (045i s 06j)
Itthe resultant of all the oxternal lorces acling on a ayslem of (b)
particles is zero, then from an inertial frame, one can Hurely
bay that (TJEE 2009)
(o) -(09j+ 12) (d)
A 100 giron ball colldesw
(a) Linear momentum of Ihe systen does not change in having velocity 10rm/s same angk
at an angle 30° and
time rebounds with the 0|se
wallis 2
perlod of contact between the ball and
(b) Kinetic energy of the system does not change in time then the force
(e) Angular momentum of the system dos not change in
experienced by the wall is
Similar CBSE
PHT

(CPMT 1997:;
time (a) 10N (b) 100 N
(d) Potential energy of the syslem does not change in time (c) 1.0N (d) 0.1N bulletof
7 A machine gun fires a bullet ol mass 40g with a veloclly 14. Abullet Is fred from a gun. The force on the ins
1200 m#, The man holding lt can exert a maxlmum lorce of by F=600-2x10t, andt kat
newtons
144 Non the gun. How many bullets can he fire per second The force on the where Fis in
sOon
it
as

barrel, WNhat is thebullet becomes

zero as bu
the
at the most IAIEER 2004;Simlar Kerala PMT 2007) impartedl toPMr
ICBSE
(a) One (b) Four average Impulse
(e) Two (d) Three (a) 9Ns (b) Zero
(c) 0,9 Ns (d) 1.8 Ns
 Newton'sLaws of Motion 195
15 A Stationary body of mass 3 kg explodes into
three equal
pieces. Two of the pieces fly off in two mutually
21. Rocket engines lift a rocket from the earth surface because
hot gas with high velocity
perpendicular directions, one with a velocity of 3i ms and [AIIMS 1998; JIPMER2001. 02: Similar CPMT 1980]
the other with a velocity of 4j ms If the
explosion occurs (a) Push against the earth
in 10 s, the average force acting on the
third piece in (b) Push against the air
newton is
(Kerala PET 2009) (c) React against the rocket and push it up
(a) (3i +4) ×10-4 (b) (3i -4)) x104 (d) Heat up the air which lifts the rocket
(c) (3i +4) x10* (d) -(3 +4,)x 10 22. The rate of mass of the gas emitted from rear of a rocket is
(e) (4i -3j) x109 initially 0.1 kg/sec. If the speed of the gas relative to the
16. Consider the following statement: When jumping from some rocket is 50 m/sec and mass of the rocket is 2 kg, then the
height, youshould bend your knees as you come to rest, instead acceleration of the rocket in m/sec is
of keeping your legs stiff. Which of the following relations can be (J& K CET 2008; Similar NCERT 1984]
useful in explaining the statement [AMU(Engg.) 2001] (a) 5 (b) 5.2
(a) AP =-AP, (b) AE=-A(PE + KE) =0 (c) 2.5 (d) 25
(c) FAt =mÂU (d) Axc AF 23. A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If
Where symbols have their usual meaning velocity of exhaust gas is 1 km/sec, then it lifts with an
acceleration of [WB-JEE 2008]
17. An explosion blows a rock into three parts. Two parts go off
at right angles to each other. These two are, 1 kg first part (a) 1000 ms? (b) 100 ms2
moving with a velocity of 12 ms and 2 kg second part (c) 10 ms2 (d) 1 ms -2
moving with a velocity of 8 ms. If the third part flies off
24. In the first second of its flight, rocket ejects 1/60 of its mass
with a velocity of 4 ms, its mass would be
with a velocity of 2400 ms. The acceleration of the rocket
[CBSE PMT 2009; Similar NEET 2013] is [BHU 2006]
(a) 5 kg (b) 7 kg
(a) 19.6ms2 (b) 30.,2 ms2
(c) 17 kg (d) 3 kg
18. A shellat rest at the origin explodes into three fragments of (c) 40 ms2 (d) 49.8 ms2
masses 1kg, 2kg and m kg. The lkg and 2kg pieces fly off 25. In arocket of mass 1000 kg fuel is consumed at a rate of 40
with speeds of 5ms along x-axis and 6ms along y-axis
respectively. If the m kg piece flies off with a speed of 6.5ms, kg/s. The velocity of the gases ejected from the rocket is
the total mass of the shell must be [Kerala PET 2007] 5x10 m/s. The thrust on the rocket is
(a) 4 kg (b) 5 kg [MP PMT 1994; Similar Odisha JEE 2005)
(c) 3.5 kg (d) 4.5 kg (a) 2x10 N (b) 5x10 N
19 Astationary bomb explodes into three pieces. One piece of (c) 2x106 N (d) 2x10° N
2kg mass moves with avelocity of 8ms at right angles to 26. If force on a rocket having exhaust velocity of 300 m/sec is
the other piece of mass lkg moving with a velocity of 210 N, then rate of combustion of the fuel is
12ms, If the mass of the third piece is 0.5kg, then its
velocity is [Kerala PET 2011] (CBSE PMT 1999; MH CET 2003; Pb. PMT 2004]

(a) 10 ms 1 (b) 20 ms1 (a) 0.7 kg/s (b) 1.4 kg/s

(c) 30 ms (d) 40 ms (c) 0.07 kg/s (d) 10.7 kg/s
27. A satellite in force-free space sweeps stationary
(e) 50 ms-1
interplanetary dust at a rate dM / dt = u where M is the
20. A shell of mass 5M, acted upon by no external force and mass, u is the velocity of the satellite and a is a constant.
initially at rest, bursts into three fragments of masses M, 2M
What is the de-acceleration of the satellite [CBSE PMT 1994)
and 2M respectively. The first two fragments move in
opposite directions with velocities of magnitudes 2V and V (a - 2av' |M (b) -av' /M
respectively. The third fragment will [WB-JEE 2013]
(a) Move with a velocity V in adirection perpendicular to (c) +au² /M (d) -au2
the other two
(b) Move with a velocity 2Vin the direction of velocity of
28. A rocket with a lift-off mass 3.5x10 kg is blasted upwards
with an initial acceleration of 10 m/s. Then the initial thrust
the first fragment of the blast is [AIEEE 2003)
(c) Be at rest
(d) Move with a velocity Vin the direction of velocity of the
(a) 1.75x 105 N (b) 3.5x105N
second fragment (c) 7.0x 10 N (d) 14.0x 10° N
 acted on by a force
of mass 3kgis
Abody the graph
below. The momentum acvat which
Newton'sLaws of Motion 35.
shown in AFIN)
196 exhaust speed
The
2Oms givenby
vertical firing.
accelerationof needed
set for
A5000 kq rocket is initial upward
(a) Zero 10
29. give an to supplythe
is 800ns. To per second (b)5N-s
the amount of gas ejected 2009)
(Q= 1Oms) Similar Odisha JEE (c) 30N-s
thrust will be 1998:
[CBSEPMT s
(b) 187.5 kg (d) 50N-s
(a) 127.5 k sl
kqs-! is initially at rest. Aforce
(d) 137.5diameter Imm. The mass 2 kg
(c) 185.5 kg s of Aparticle
of changes with time. The force
waters the plants bya pipe
cm'/sec. The
reactionary 36. magnitude
10 (KCET 2000) whose
30. A gardner out at the rate of is shownbelow
comes gardner
water hand of the
(b) 1.27x10N F(N)
force exerted on the
(d) 0.127 N 20
(a) Zero by
(c) 1.27x 10N mass m is indicated
particle of The change
F acting on a below.
The force shown from zero to 10|
31.
force-time graph overthe time interval
(CBSE PMT2014J
the particle ts
momentum of the 6 10
0 2
8s is [(Kerala PET 20%
particle after 10s is
The velocityofthe (b) 10 ms-l
(a) 20ms-l
4
(d) 26 ms-!
(c) 75 ms-l

(e) 50 ms acted upont

(b) 6 Ns m, initially at rest, is
mass It beginstom
(a) 12Ns (d) 20Ns
shown 37. Aparticle of brief interval of time T.
shown
a
(c) 24 Ns particle of mass 4 kg is variable force F for force stops acting. Fis
a time u after the semicircde.
position-time graph of impulse (in MKS units) at with avelocity curve is a
32. The Calculate the (AMU (Engg.) 2012] function oftime. The
in the figure. respectively graph as a
seconds
t=0and t =6
+6.31and - 6.31
x(m)5 (a) u=
(a) 2m
(b) +3.33and-3.33
(b) u 8m
(c) +5.25and-5.25 6 ’t(s)
Time
(d) +3.25and-3.25 partice of (c) u
position-time graph ofa
2005)
4m
given below, the sec is (AIIMS
33. In the figure shown.The impulse at t= 2 (d) u= 2m
F,T intiuen
the
mass 0.1 kgis plane under momentum
x(m) the X-Y
0.2 kg msec-1 38. A particle moves in linear
(a) 6 that its are
conN

sec force such and k

-0.2 k m 4 where A
(b)
2 Pt) = Ai cos(kt)-j sin(kt)], momentum is
(ITJEEAN
sec-1 t(sec) andthe
0.1kq n force
(c) 2 4 6 The angle between the
(d) -0.4
kq msec 5ms. A force acts on it (b) 30°
initialspeed time
body of 2 kq has an of motion. The force (a) 0° (d) 90° ofa
A direction bod. action
34. time in the speed of the
for somne The final (c) 45° underthe
in figure. x-y plane momentum P)
atas
qraph is shown 39. A particle moves in the
FN)| linear
such that the value of its [MNR1991:UPSEATA
t. The angle
t is P, = 2cost, p = 2sin
at a given time t, will be = 30
4 45 6.5 ((s) (b)
(a) = 0° =180°
(b) 5ms! (d)
! (c) 0= 90
(a)
9.25 ms ! (d) 4.25 ms
14.31ms !
(c)
 by the wall on the ball will be third force rg
The value of impulse imparted

-
F.
me F.
(b)
(a) F.
F
60 F,
60
F
(NEET (Phase-II) 2016] (d)
(c) Fz
mV
(a) m (b)
3
2 correct order of forces
(d) 2mV 5. Which of the following is the [AIEEE 2002]
(c) mV
(nuclear) <
is divided in two parts. One
part gravitational forces < strong forces
41. An explosive of mass 9 kg kinetic (a) Weak <
velocity of 16 m/s. The
of mass 3 kg moves with
electrostatic
force
energy of other part will
be
[WB-JEE 2016]
weak<(electrostatic) < strong
(b) Gravitational <
(b) 162J electrostatic < weak < strong force
(a) 192J (c) Gravitational <
electrostatic < strong forces
(c) 150J
(d) 200 J (d) Weak < gravitational <
simultaneously on a particle moving
molecule is 3.32 × 10-2 k. If 1023 6. Three forces starts acting
The mass of a hydrogen are represented in magnitude
42.
second a fixed wall of area with velocity k. These forces
hydrogen molecules strike, per of a triangle ABC (as shown).
and direction bythe three sides
2 cm at an angle of 45°
to the nomal, and rebound velocity [AIEEE 2003]
The particle will now move with
then the pressure on the
elastically with a speed of 10° m/s, (a) v remaining unchanged
[JEE (Main) 2018]
wall is nearly
(b) Less than
(a) 2.35x 10²N/m² (b) 4.70 x 10 N/m?
(c) Greater than u A B
(c) 2.35x 10° N/m² (d) 4.70 x 10 N/m?
largest force BC
(d) u in the direction of the
Equilibrium of Forces inclined plane of 1 in I. The
7. An object is kept on a smooth
inclined plane
a resultant of the same horizontal acceleration to be imparted to the
1. Two forces of magnitude F have to the inclined is
magnitude F. The angle between the
two forces is sothat the object is stationary relative
(UP CPMT 2006]
Similar MP PMT 1999]
[CBSE PMT 1990; MP PET 2012;
(b) 120° (a) gi?-1 (b) g(l -1)
(a) 45°
(d) 60
(c) 150 (c) (d)
2-1
1 N, 2 N and3 N acting Jie-1
2. Three concurrent co-planar forces
(KCET 2009] magnitudes is 18 N
along different directions on a body 8. Two forces are such that the sumn of their
smaller force and
equilibrium if 2N and 3 N act at and their resultant is perpendicular to the
(a) Can keep the body in of the
magnitude of resultant is 12 N. Then the magnitudes
right angle [AIEEE 2002]
forces are
equilibrium if 1 N and 2 N act at
(b) Can keep the body in (a) 12 N, 6 N (b) 13 N, 5N
right angle (d) 16N, 2N
(c) 10 N, 8 N
(c) Cannot keep the body in equilibrium 9. When forces F1, F2, F3 are acting on a particle of mass m
equilibrium if lN and 3 N act at such that F2 and Fs are mutually perpendicular, then the
(d) Can keep the body in
an acute angle particle remains stationary. If the force Fi is now removed
not be [RPET 2000) then the acceleration of the paticle is [AIEEE 2002]
3. The resultant force of 5Nand 10N can
(a) 12 N (b) 8N (a) F/m (b) FF_ImF
(c) 4N (d) 5N (c) (F, -F)/m (d) Fz/m
 weights A, B and C of mass 2
198 Newton's Laws of Motion Three equal kg
string passing over afixed
10. A block of mass m is placed on a
smoothinclined
as shown in the fiqure. The
wedge
wedge is
4
hanging on a
shown in the is
and C
figure The tension in the
(MP PET 1985;
ficistoninlegsS coNeplaehk
ABCof inclination
given an acceleration 'a
towards the right. The relation
weights B
SCRA I
remain stationary On
for the block to
between a and
wedge is (a) Zero
A (b) 13N
m (c) 3.3N
(d) 19.6N

Ablock A of mass 7 kg is placed on a frictionless tae

5. thread tied to it passes over a frictionless pulley and carie
(NEET 2018]
body B of rmass 3 kg at the other end. The acceleratig
g= 10 ms 2) [Kerala (Engg) 20%
(b) a = sin the system is (given
(a) a = COs ecO
-2
(a) 100 ms
a=gcos (d) a= gtan
(c)
(b) 3ms-2
Motion of Connected Bodies (c) 10ms2
B
the
and 4 kg are suspended at
1 Two bodies of mass 3 kg
passing over a frictionless pulley.
The (d) 30ms -2
ends of massless string is accelerating downward
m/s) A body shown in figure
acceleration of the system is (g =9.8
6.
the string is
PMT 2001] acceleration 2 m/s. The tension in
[MP PET 1994; CBSE [Odisha JEE 208
(b) 2.45m/s? r=10
(a) 4.9m/s? (a) 48 N
(d) 9.5m/s?
(c) 1.4 m/s? (b) 50 N 12ko
by
m,m and m, are connected (c) 30 N
2 Three blocks of masses
They are 37°
a frictionless table. (d) 42 N
massless strings as shown on the
If m, =10kg, m, =6kg
and is suspended as shown in
'pulled with a force T; = 40N.
7 A body of weight 2ka string (in kg wt) 15
[MP PMT/PET 1998; The tension T, in the horizontal
tension T will be [KeralaPMT20:
m, =4 kg , the
EAMCET 1983) 30°
Odisha JEE 2008; Similar T
(a) 2/V3
(b) V3/2
(c) 2V3
2 kg-wt
(b) 40 N
(a) 20 N (d) 2 Over a
naN

(d) 32 N passes whilethe

One end of a massless rope, which hook
(c) 10N Ccan bears
frictionless and frictionless pulley P is tied to a
pulled along a horizontal
Ablock of mass M is applied at #ha end is free. Maximum tension that the
rope (inns
mass m. If a force P is
3. acceleration
surface by a rope of N. with what value of minimum safe
exerted by the rope on the rope
rope, the force down on the
free end of the (CPMT 1972, 75, 82:
can a monkey of 60kg move (AIEEE
2
block will be
AIEEE 2003I
CRSE PMT 1993; MP PMT 1996;
(a) 16
Pm
(b) M+m (b) 6
(a) P
Pm (c) 4
PM (d)
M-m (d) 8
(c) M+ m
 Newton's Laws of Motion 199

Alight string passing over a smooth light pulley connects two 14. Two bodies AandBof masses 10 kg and 15 kg respectively
blocks of masses m, and m, (vertically). If the acceleration of kept on a smooth, horizontal surface are tied to the ends of
the sustem is g/8 then the ratio of the masses is [AIEEE 2002] a light string. If T represents the tension in the string when a
horizontal force F 500 N is applied to A (as shown in
(a) 8: 1 (b) 9:7 fiqure 1) and T' be the tension when it is applied to B (figure
(c) 4:3 2), then which of the following is true [AMUPMT 2009)
(d) 5:3

Two masses m = 5kg and m, = 4.8kg tied to a string are 10 kg 15 kg

F=500 N
A B
hanging over a light frictionless pulley. What is the
acceleration of the masses when they are free to move
10 kg 15 kg
(g = 9.8 m/s) [AIEEE 2004; Similar Odisha JEE 2002] A B
F=500 N

(a) 0.2 m/s?

(a) T =T'=500N (b) T=T= 250N
(b) 9.8 m/s
(c) T = 200 N, T= 300 N (d) T= 300 N, T= 200 N
(c) 5 m/s2
15. A block of mass M placed on a frictionless horizontal table is
m pulled by another block of mass m hanging vertically by a
(d) 4.8 m/s? m
massless string passing over a frictionless pulley. The tension
in the string is (MP PET 2010]
|1. Two block of masses 7 kg and 5 kg are placed in contact
with each other on a smooth surface. If a force of 6 N is m M
(a) (b g
applied on the heavier mass, the force on the lighter mass is M+m M+m
[Kerala PMT 2008; WB-JEE 2010; Similar MP PET 2012) M+m Mm
(c) (d)
(a) 3.5N 7kg Mm M+m

(b) 2.5N 5kg

16. Three blocks of mass 4kg, 2kg, lkg respectively are in
6N
contact on a frictionless table as shown in the fiqure. If a force
(c) 7N of 14 N is applied on the 4kg block, the contact force
(d) 5N between the 4 kg and the 2kg block will be
(e) 6N [WB JEE 2012, AIPMT (Cancelled) 2015)
12. Consider the following statements about the blocks shown in
the diagam that are being pushed by a constant force on a 14N 4 kg 2 kg 1kg
fictionless table
(a) 2N (b) 6N
3kg
2 kg (c) 8N (d) 14 N
1 kg
17. A block of mass 15 kg is held by astring on an inclined
A Alblocks move with the same acceleration plane (angle 30°). The tension T in the string is
(g =10 mn/s) [AMU (Engg.) 2012]
B. The net force on each blockis the same
Which of these statements are is corect [AMU (Engg.) 2001] (a) 55 N
M=15kg
(b) 60 N
a) A ony (b) B
only
(c) 75 N
c) Both A and B (d) Neither A nor B
(d) 90 N K30P
13. A block of mass 'm' is connected to another block of mass
18. Three blocks with masses m, 2rm and 3rm are connected by
M by a spring (massless) of spring constant k. The blocks strings, as shown in figure. After an upward force F is
are kept on a snooth horizontal plane. Initially the blocks applied on block m, the masses move upward at constant
are at rest and the spring is unstretched. Then a constant speed u. What is the net force on the block of mass 2n (g is
iorce F starts acting on the block of mass 'M to Dull it Find the acceleration due to gravity) [NEET 2013]
the force on the biock of mass 'm [AIEEE 2007)
(a) 6 mg
m (M + mF)
a b) (b) Zero
M m

MF
(c) 2 mng 2rn
mF (d)
m- M (d) 3 mg 3rn
 200 Newton's Laws of
Motion
What ia
Unstotfoe , where
slnd passl over a rictionlesS ulley. As shown
stioolh inclined
(Un edte
ls plaeedon n
19. homthee d2000l the masg the syslem is
oe al a etnce 106,97,
the tension h the (MI PET an cceleralion equalto (AMU
the loe is apied blocks OVe wilh
I(0.)
(b)
(a) (a) 4/4
(b) g/3
()
(c) g/2
30
A block of weight 4 ku is
restins 2k !
20. of water nt
thevate of (d) g bodies
plane, I i e struck by a jet acceleration of systerm of two 0ver he Wet,
initol acceleratlon of The
10m . then the |Kerala PET 2012] 26. (Odisha JE
and at the speed of shown in fiqure is
the block is
(b) 10ms
(a) 15ns

(c) 2.5ms
(d) Ims 53
(e) 5ns
(b) 2ms 2
the
as shown in (a) 1ms-2
are connected by a string A force
Two blocks another string. (d) 10ms 2
21. block is hung by acceleration of (c) 0.5ms2
diagramn. The upper string produces an
upper and T" ends P and 0
Fapplied on
the
direction in both the blocks, If T thern arrangerment shown in figure the
Zm/s in the upward the two parts of the string, 26. In the downwards with uniform
tensions in unstretchable string move M moves upwards
be the Kerala PET 2010] fixed. Mass
(g=9.8 m/s?) (AMU(Engg.) 2000; U. Pulleys Aand
B are
speed
and T'= 47.2N 2 kg
(a) T=70.8N (a) 2U cos 0 AK
47.2N
T=58.8N and T = (b) Ucos
(b)
T'=58.8N
70.8NV and
(c) T= 4 kg 2U
T=70.8N and
T'=0 (c) COs P
(d) respectively, are
and B of masses 2rm and m, The whole U
Two blocks A massless and inextensible string. (d)
22.
connected by a shown in the COs
by a massless spring as A and B. shown in the figure are
Smo
systern is suspended
nagnitudes of
acceleration of
27. The pulleys and
strings in ecuilt
remain
respectively systemto
fiqure. The
string is cut, are negligible mass. For the (uTJEE
immediately after the 2017]
(iIT-JEE 2006; NEET the angle should be
(a) 0°
(a) g. g2 (b) 30°
(b) g2, g
(c) 45°
(c) g.g puley
ideal. the (d) 60° clamped
(d) g2, g2 pulleys are fixed and Over a fiqreT
arrangenent shon, the balance which is 28. Astring of negligible mass going showninthee (ITJEE
In the m and S is a spring mass Mas
23.
stríngs are light, m
>
is (DCE 20061 msupports a block of
S (in unit of mass) given by
teef rnassless. The reading of on the pulley by the clamp is
(a) m -my (a) V2Mg
L(m +rnz) (b) /2mg
(b) 7
(c) V(M +m)? +m'g
(c)
(d) y(M+ m) +Mg
2n;my
(d)
 Newton's Laws of Motion 201

29.
The masses of 10 kg and 20 kg respectively are connected 33. Two identical objecis each of radi R and masses m and
by amassless spring as shown in fiqure. A force of 200 N as
ats on the 20 kg mass. At the instant shown, the 10 ka rnass m, are suspended using two strings of equal length L
has acceleration 12 m/ sec What is the acceleration of 20 shown in the figure (R << L). The angle which mass mz
makes with the vertical is approxirnately (KVPY 2015]
kg masS
20 kg 200N
10 kg

(a) 12 m/ sec (b) 4 m/sec?

(c) 10 m/sec? (d) Zero
30. Aspring balance and a physical balance are kept in a lift. In
these balances equal masses are placed. If now the lift starts m,R
moving upwards with constant acceleration, then (a)
(m, + m,)L
(a) The reading of spring balance will increase and the
equilibrium position of the physical balance will (b)
2m, R
disturb (m, +m, )L
(b) The reading of spring balance will remain unchanged 2m,R
and physical balance will remain in equilibrium (c)
(m, + m,)L
(c) The reading of spring balance will decrease and
physical balance will remain in equilibrium (d) m,R
(d) The reading of spring balance wll increase and the (m, +m,)L
physical balance will remain in equilibrium 34. Three blocks, of masses m, =2.0, m, = 4.0 and
31. As shown in the figure, two equal masses each of 2 kg are
suspended from a spring balance. The reading of the spring m, =6.0 kg are connected by strings on a frictionless
balance will be inclined plane of 60°, as shown in the figure. A force
F-120 N is applied upward along the indine to the
(a) Zero uppernost block. causing an upward movement of the
(b) 2 kg blocks. The connecting cords are light The values of
(c) 4 kg 2kg 2kg tensions T, and T, in the cords are [AMU (Med.) 2012]
(d) Between zero and 2 kg
32. Two block (1 and 2) of equal mass m are
connected by an ideal string (see figure
below) over a frictionless pulley. The
blocks are attached to the ground by
springs having spring constants k, and kz 600
such that k, > kz:
Initially, both springs are unstretched. The
block 1 is slowly pulled down a distance x (a) T =20N, T, = 60 N (b) T, = 60 N. T, = 60 N
and released. Just after the release the
possible value of the magnitudes of the
(c) T = 30N, T, = 50 N (d) T, = 20 N, T, = 100 N
acceleration of the blocks a, and a, can 35. Two masses m, =5kg and m, =10 kg connected by an
be (KVPY 2012] inextensible string over a frictionless pulley are moving as
(a) Either a =a, = k, +kal) --g and shown in the figure. The coefficient of friction of horizontal
2m m
surface of 0.15. The minimum weight m that should be
put on top of m, to stop the motion is [JEE (Main) 2018)
m

(b) (k, +kz)x only

2m

-kelx
(c)a, =a, - k2rn only

(d) Either a =a2= (ky2rm

-ka) or
m,g

(kjkz) (a) 43.3 kg (b) 10.3 kg

(k, +kzjm (c) 18.3 kg (d) 27.3 kg