suddenly disintegrates

particle into two

at rest which start moving. The
5.4 Physics
mass of a
rocket going
45. A
of cqual
masses
direction with
two fr
of time thecjccting 5 kg of gas per will: same equal
certain instant
If it is aceeleration of the move in the direction with any speed Spee 51. Ashell of mass 20
39. A a is 100 kg. (a) If the muzzle
up verticallvspeed of 400 m/s, the in any speec
(b) move opposite directions with equal
unequalspees
sOnd at a l0 nn/s) speed of the gun is
rChet wouldbe
(taking g (b) 10 n/s (c) moveinopposite directions with (a) 16 cm s
(a) 20 m's* (d) I m? (d) movein an aparticle.
In (c) 8 ms
(c) m's
ofmetal
on a frictionless
weighing 2 kg is resting a rate of l kg/s 46. A nuclide
at rest emits
a-particle noves
with large velocitythisandprocthe 32 A 100 kg gun fire
40. A block strck by a jet relcasing water at of the block (a) remains at rest of height 500 m.
plane. It is acceleration mnove wih m from the bottC
and a spd of Sms. The initial
(b) both o-particle and nucleus equ gun is (Take g: 1
(b) S m/s in opposite directions
directions (a) 0.2 ms
(a) 25 m s (d) 20 m/s in opposite but nuce
() 10 ms (c) both move (c) 0.6 ms!
greater speed
going up. The total (d) both move in opposite directions but a-partis 53. Abody of mas=
41. 1lit is peeds
b9S/w u of which of mas
and the
ass of the lit greater speed.
Pssenger is 1500 kg.
The directions with
the 47. Avessel at rest explodes breaking it into three The third piec
Va7310n in the speed of Two pieces having equal mass fly off perpendi
lift is as given in the graph. (a) 1.5 m/s
The icnsion in the rope 10 12 speed of 30 m/s. The s (c) 2.5 m/s
= 1lth one another with the same
pulling the lift at bas three times the mass of each other piece 54. A bullet is fir
the direction (w.r.t. the pieces having equal mas
se will be
(a) 17400 N (b) 14700 N given by F=
ic) 12000 N (d) Zero magnitude of its velocity immediately after the e t in seconds
(b) 10/2,90 SOon as it lea
abody of mass m at rest. (a) 10/2. 135°
42. A constant force starts acting on imparted to
distance
The velocity acquired in traveling a specific (c) 10/2, 60° (d) 10/2, 30° (a) 9 NS
depends on m as (c) 0.9 Ns
1
(b) vo« 48. A radioactive nucleus initialy at rest decays by
an electron and neutron at right angles to one 55. A particle
(a)
ym
force F suc
(c) xm (d) vocym The momentumn of the electron is 3.2 X 103 kgm p at any tir
43. Match Column Iwith Column II and mark the correct the momentum of neutron is 6.4 x 1025 koml between F
direction of the recoiling nucleus with that of the (a) 90°
choice from the given codes.
motion is: (c) 180°
Column-I Column-II
(a) -tan (2) (b) tan (2)
(A) Definition of force (p) Newton's third law 56. Figure sh
(B) Measure of force (c) tan (0.5) (d) + tan (2) dimensiot
(q) Impulse 2 time inter
(C) Efect of force (r) Newton's second law 49. A shell is fired from a cannon with velocity v ms by the bo
(D) Recoiling of gun (s) Newton's first law angle with the horizontal direction. At the highes x (m) 4
Codes in its path it explodes into two pieces of equal mas
(a) A-q. B- p, C -, D-s of the pieces retraces its path to the cannon and the
(b) A-p, B- 9, C-r, D- s inm/s of the other piece immediately after the explos 2+
(c) A-s, B-r, C-q, D-p (a) 3v cos
(d) A-s, B-q, C- r, D-p (b) 2v cos 0
3v
Linear Momentum and Impulse (c) cos
(d)
V3v cos e
44. Which one of the
following 50. Three
2 (a) 2=
(a) The same force for the statements is not true? particles A, B and C of A (c) 6=
same time causes the same equal masses move with equal
change in momentum for different bodies. 57. Figure
(b) The rate of change of speeds v along the medians of mass

proportional momentum of a body is directly

to the applied an equilateral triangle. They S, t>
the direction in which the force and takes place in collide at the centroid O of
(c) Agreater force acts. the triangle. After
opposing force
comes to rest whilecollision
is needed to stop a A
body than a light body in the heavy B retraces
moving with the same time, if they are its path with speed v. The
Bé
(d) The greater the same speed. velocity of C is then
time, the lesser ischange in the
the force thatmomentum in a (a) v, direction OÁ
needs to be given applied. (c) 2v, direction OB
(b) 2v, direction 0
(d) v, direction BO
 Newton's Laws of Motion $.5

S1 A shell of mass 200 g is fired by a gun of

mass 100
If the muzzle speed of the shell is 80 ms, then the kg. (a) F = F=F= 0 (b) F> F,= F;
recoil (c) F, > F;> F (d) F <F,<F
speed of the gun is
(a) 16 cm s (b) 8 cm s 58. In the figure given below, the position-time graph of a
(c) 8 ms! (d) 16 m s particle of mass 0.1 kg is x(m)
52. A 100 kg gun fires a ball of 1kg horizontally from a cliff shown.The impulse at =2 6
of height 500m. It falls on the ground at a distance of 400 sec is
A
m from the bottom of the cliff. The recoil
velocity of the (a) 0.2 kg m sec 2
gun is (Take g: 10 ms)
(a) 0.2 ms (b) -0.2 kg m sec 6(sec)
(b) 0.4 m s! 2 4
(c) 0.6 ms! (d) 0.8 ms (c) 0.1 kg m sec
53. Abody of mass M at rest explodes into three pieces, two (d) -0.4 kg m sec
of which of mass MI4 each are thrown off in 59. A body of 2 kg has an initial speed 5 ms. A force acts
directions with velocities of 3 m/s and 4 m/sperpendicular
The third piece will be thrown off with arespectively.
on it for some time in the direction of motion. The force
velocity of time graph is shown in figure. The final speed of the
(a) 1.5 m/s (b) 2.0 m/s
(c) 2.5 m/s body is
(d) 3.0 m/s
F (N) 4
54. A bullet is fired from a gun. The force on the bullet is
given by F =600 -2 × 10° 1, where F is in newtons and
in seconds. The force on the bullet becomes zero as 4

sOon as it leaves the barrel. What is the average impulse

imparted to the bullet? 2.5
(a) 9 Ns (b) Zero
(c) 0.9 Ns 2 4 4.5 6.5
’t(s)
(d) 1.8 Ns
55. A particle moves in the xy-plane under the action of a (a) 9.25 ms (b) 5 mns!
force F such that the components of its linear momentum (c) 14.25 ms (d) 4.25 ms
p at any time are p, = 2 cos t, p, = 2 sin t. The angle 60. A force time graph for
between F and p at time t is the motion of a body is 1
(a) 90° (b) 0°
(c) 180° shown in the figure. The
(d) 30°
change in the momentum
56. Figure shows the position-time (x-t) graph of one of the body between zero (N) 8 10;t (s)
dimensional motion of a body of mass 500 g. What is the and 10 sec is 0.5
time intervalbetween two consecutive impulses received (a) zero (b) 4 kg m/s
by the body?
(c) 5 kg m/s (d) 3 kg m/s
x (m) 4
61. A2 kg toy car can move along an x axis. Graph shows
force F, acting on the car which begins at rest at time
2
=0. The velocity of the particle at = 10 s is:
F&(N)
2 4 10
12 (9) 4

(a) 2 s (b) 4 s
(c) 6s (d) 8 s
57. Figure shows the position-time graph of a particle of 0
4 9 10 1(s)
mass 4kg. Let the force on the particle for <0, 0<<4
5, 1>4s be F,F, and F, respectively. Then
x (m) 4
(a) /s (b) -1.5 ims
(c) 6.5 im/s (d) 13im's
3
62. A purticle of mass 'n' and initially at rest is actd by
u force F- a Newtons best represcntation ot ne
displacenment graph iN:
 placed on a smooth
5.6 Physics mass 2.0 kg is
67. A body of forces F, = 20 N
and P,
surface. Two
the body in directions making
angles of 30° are =N ac
surface.
the
The reaction
of surface on the and 6
(a) (b)
body
F1
Z60°
30C- 2 kg

(c) (d)
(a) 20 N (b) 25 N
(c) 5 N (d) zero
a smooth
63. A 15 kg block is initially moving along co-planar forces 1 N, 2 N
horizontal surface with a speed ofy=4 m/s to the left. It Three concurrent
IS acted by a force F, wvhich varies in the manner shown. 68.
along different directions on a body and 3N
Determine the velocity of the block at = 15 seconds. (a) can keep the body in equilibrium if 2] Nand
AF()
at right angle.
equilibrium if 1 N
(b) can keep the body in and
40 at right angle.
equilibrium
F 10 (c) cannot keep the body in
5 15 (d) can keep the body in equilibrium if 1 Nand 3
t(s)
at an acute angle.
69. In the figure shown °P is aplate on which a We
Given that, F = 40 cos nlaced and on Ba block A of mass m is placed. 7
(a) 12.5 m/s (b) 8.5 m/s is suddenly removed and system of Band Ais.
(d) 9.5 m/s
to fall under gravity. Neglecting any force due to
(c) 20 m/s
A and B, the normal force on Adue to B is
A
Equilibrium of a Particle m

64. A body subjected to three concurrent forces is found to be

in equilibrium. The resultant of any two forces B
(a) is equal to thirdforce
(b) is opposite to third force mg
(b) mg cos
(a)
(c) is collinear with the third force cos

2mg
(d) allof these (c) zero (d)
cos
65. A block of mass 3kg is at rest on
a rough inclined plane as shown 70. Which of the following sets of concurrent forces m
in the figure. The magnitude of in equilibrium?
net force exerted by the surface (a) F =3N, F, 5 N, F, =9 N 75
on the block will be (b) E, =3N, F, = 5 N, F; = 1N
(a) 26N (b) 19.5 N (c) F =3 N, F, = $ N, F, = 15 N
(c) 10N (d) 30 N (d) E, =3 N, F, =S N, F;=6 N
66. A body of mass | kg lies on
m= 1kg
71. A uniform sphere of weight W
smooth inclined plane. The and radius 3 m is being held by a
block of mass mis given Wall
F= 10N string of length 2 m. attached to a
force F= 10 Nhorizontally as frictionless wallas shown in the
45°
shown. The magnitude of net
normal reaction on the block is:
figure. The tension in the string
will be:
(a) 10V2 N 10 (a) 5 W/4 76
(b)
(b) 15 W/4
(c) 10N (d) none of these (c) 15 W/16
(d) none of these
 Newton's Laws of Motion 5.7

72.A metal sphere is hung by a

string fixed to a wall. The forces (a)
acting on the sphere are shown 2N
11 N
in figure. Which of the following 3
45
45°
statements is NOT corect?
(a) N+Y+W =0 p
(b) T= N² + "90
(c) T= N+ W
Wall W 3 3
(d) N= Wtan (d) N

73. Figure shows a man of mass 50 kg standing on a light 77. In the following
weighing machine kept in a box of
mass 30 kg. The box is hanging from figure, the pulley P
a pulley fixed to the ceiling through a is fixed andthepulley A Pi
P, is movable. If W
light rope., the other end of which is = W, = 100 N, what
held by the man himself. If the man
manages to keep the box at rest, the is the angle AP,P?
The pulleys are
weight shown by the machine is. W
(a) 10 N frictionless.
(a) 30° (b) 60°
(b) 100 N (c) 90° (d) 120°
(c) 800 N
(d) 200 N 78. The pulleys and strings shown in the figure are smooth
and of negligible mass. For the system to remain in
74. Aweight Wissupported by two strings inclined at 60 and equilibrium, the angle should be
30° to the vertical. The tensions in the strings are T, and
T, as shown. If these tensions are T.
to be determined in terms of W
60
using a triangle of forces, which
of these triangles should you
dra w? (block is inequilibrium)

(a) wY V2m

(b)
(a) 0° (b) 30°
(c) 45° (d) 60°
79. Astring of negligible mass going over a clamped pulley
of mass m supports a block of mass M as shown in the
(C) (d) figure. The force on the pulley by the clamp is given by
wT
m
75. A block of mass 5 kg is
suspended by a massless rope 1m
of length 2 m from the ceiling. P
A force of 50 N is applied 50 N
in the horizontal direction at 1m
the midpoint P of the rope, as
M
shown in the figure. The angle
made by the rope with the 5 kg
vertical in equilibrium is (Take g= 10 ms) m
(a) 30° (b) 40°
(c) 60° (d) 45°
76. There are four forces acting at a point P produced by (a) V2Mg (b) V2mg
strings as shown in figure, which is at rest. The forces F,
(c) J(M + m)²+ m²g () yM +m +M'g
and F, are
 84.
Applications 83.
4.(c0) m2.(a8) mit isasmooth 82.
just
nd smooth a mMis (c)kg 5 (a )
15
kg longer
to is S1.
wil tightly Two tan(I/3N3)(c) (1/2)
t
(anprevent
) The
surfaces 80.
m,
light and
completely attached arranged
cylinders Three (d) (c) (b) cylinder
(a) are:
the
spheres 8
travel a cm. fixed WTwO =1+(d)tan 8=1+ta(cn) =1+t(abn) =1+t(an)
released, =and string. m, fixed remains persons
at least 3W/
W4 W74 WW4 rest For Tvo
and Physics5.8
7.5 are its the identical and The
smooth smooth
one the and Tm
wedge. of as on and and and
in fixed. the
2the kg. The
connected
toends
arrangement value shown A, Wand reactions systemmasses
m, straighten
horizontal. th e are
Newton' s smooth the on
seconds When pulley B
rigid 3WI4 W/4 3WI4 cylinder spheres
distance =10 wedge Masses rope holding so the 2M m 2m M
that of in and vertical M 2n 2M to
at inclined circular
figure. between other be
is m,kg is is by the The in
Mare
the it is a Laws from that are C of each
6.(d0) m(7.b5) m rope horizontal. rope
side radiusinside cquilibrium
Infinitely
large(d) 15/(b2kg
) minimum mid (tban) of attachcd
30 tan(1/4/3)
of (d) collapse of the a
is: point of radius
Motion
A
tensionwhichnegligible nw2/3) is 5 45 we
with
15 cm mO havestrings
required how kg and
weightweight 45° as
|m2 weight M
no shown.
89. 88.
shown)
comparison
from figureand BI4 or be Consider
the 87. 86. 85.
150(d) N600(c) N300(b) N200(a) Nweights Mass the In (c)80
g=10ms2 kg
kg(a)40 ) (b4N
Ig
fixed light;friction
rope the weimachi
ghinngeplis:ane on ofAn(d) 8N(c6N ) (a) Ta2Nke the A of The Bg/(c)4 (gla)4 floor ofbox With
and of given a 6 = 2 descending mass of
vertical the the of the to haviweighing
ng m/s.elevator blgock 0.5 ms
clevator of
= what
options
betweenfigure Tc string to three hold
plank, man diagram, l0 Akg. The Mexert
the sfigure
be be 60° Inside is
angle box? moving
rope isthe
the wall absent cases accelerating m/s onThe withshown acceleration
Crespectively. connecting 80
machine it the force mass an a
below. the tension to plank of a
and kg. with of force up
given be given
everywhere inclination person
Weighing >
bloexert
6mila=s? the
ck accel
light pulley.
Neglect inwhat which ed eration in figure 7 so 'a
tensions
in the in position? (d50
kg
) 160(b)kg upwards
of B block Mg/4 that
the and figures force ismass is: by ) g/(b2) shoul
the d
Then blocks Take the reading60. is (d4g
strings and machine kept on
inextensible must The accele
withan
(for pick 50 thoblocl t
tothshown.
e on ke B A
the the in other puisg the
ig As
an is
man :
 Newton's Laws of Motion 5.9

93. Two masses of Ikg and 5 kg are attached LILLILU

Ikg to the ends of a massless string passing
over apulley of negligible weight. The
pulley itsclf is attached to a light spring
2kg (2kg balance as shown in figure. The masses
start moving during this interval: the
Fig. (A) Fig. (B) reading of spring balance will be:
(a) more than 6 kg
2kg (b) less than 6 kg 1 kg
(c) cqual to 6 kg
(d) nonc of the above |5 kg
Tkg 94. Three equal weights A, B, C of mass 2
kg each are hanging on a string passing L
Fig. (C) over a fixed frictionless pulley as shown
(a) T,-Tg-Tc (b) T=Te<T, in the figure. The tension in the string
(c) T,<T,<Te (d) T;< Te<T, connecting weights Band C is:
90. Consider the system as shown in the figure. The pulley (a) zero
and the string are light and all the surfaces are frictionless. (b) 13 N A

The tension in the string is (g = 10 m/s) (c) 3.3 N B

(d) 19.6 N
95. Two bodies of mass 4 kg and 6 kg are
1kg attached to the ends of a string passing C
Horizontal surface over a pulley. The 4 kg mass is attached
to the table top by another string. The
1ka
tension in this string T, is equal to: Take
g=10 ms?
(a) 0N (b) 1N (a) 20 N (b) 25 N
(c) 2N (d) 5N (c). 10.6N (d) 10N
91. Aboy and ablock, both of same mass, 96. Figure shows two pulley arrangements
4 kg
are suspended at the same horizontal for lifting a mass m. In case-1, the mass
level, from each end of a light is lifted by attaching a mass 2m while
string that moves over a frictionless in case-2 the mass is lifted by pulling 6 kg
pulley as shown. The boy starts the other end with a downward force
moving upwards with an acceleration 10 m F=2 mg. Ifa,and a, are the accelerations
2.5 m/s relative to the rope. If the of the two masses then (Assume string is massless and
block is to travel a total distance m pulley is ideal)
m
10 m before reaching at the pulley,
the time taken by the block in doing
So is equal to:
(a) V8s (b) 4 s
10
(c) (d) 8 s
F= 2mg
m 2m m

92. In order to raise a mass of 100 kg a man of mass Case-1 Case-2

60 kg fastens a rope to it and passes the rope over a
(a) a, ab (b) a, = ay2
smooth pulley. He climbs the rope with acceleration (c) a, = /3
5gl4 relative to the rope. The tension in the rope is: Take
(d) a, = 2a,
8=10 m/s? 97. In fig., the blocks 4. B and Cof mass m each have
(a) 1432 N (b) 928 N accelerations a , a, and a, respectively. F, and F) are
(c) 1219N
external forces of magnitudes 2mg and mg respectively.
(d) 642 N Then
 5.12 Physics
118. A body of mass 2 kg is at rest on a
114. A block of mass m is
coefficient of friction between the body horizontal
and table,
kept on a wedge of
mass M. Initially the M
m
0.3. Aforce of 5 Nis applied on the the table
body. The
friction is
Systenm is held. At
(a) 5 N (b) 5.88 N
certain time the system
(c) 6 N (d) 20 N
is released and the
wedge is observed to 119. A block of mass 3 kg is placed on a rough
move with acceleration 4 on inclincd surface as shown.
There is no friction anywhere. The acceleration of block
surface (u, = 0.4). A force of 8.7 Nis
block. The force of friction between the
(a) 8.7N (b) 12 N
on
and flo
applied
block horizon
(m) with respect to wedge (M) will be
(a) Arightward (b) A cos Orightward (c) 10 N (d) zero
(c) A cos leftward (d) none of these 120. A horizontal force Facts on the block
of mass m and the block remains
15. Ablock of mass m, lies on a smooth horizontal table and stationary, the value of friction force
is connected to another freely hanging block of mass is
m, by a light inextensible string passing over a smooth (a) u mg (b) u mg F
fixed pulley situated at the edge of the table. Initially the (c) F (d) zero
system is at rest with m, a distance d from the pulley.
Then the time taken for m, to reach the pulley is 121. In previous question, if we pull the
block by the force F making an angle m

and the block remains stationary, the

value of friction force is
(a) umg (b) Fcos
umg umg
(c) (d)
sin + ucos
m2
122. In ). 120, the minimum force F required to pull
(a) (b)
|2d(m, + m,)
is:
myg

2m,d mg
(c) (d) None of these (a) (b) mg
2 -cos
V(m, + m, )g 2

mg
Basic Concept of Static and Kinetic Frictions (c) (d) none of these

116. A rectangular wooden block 5 cmn × 10 cm x 10 123. Ablock of mass m is stationary on

cm in a
m
size is kept on a horizontal surface with its face of horizontal surface. It is connected
largest with a string which has no tension. The coeffhicient of
area on the surface. A minimum force of 1.5 N
applied friction between the block and surface is m. Then, the
parallel to the surface sets the block in sliding motion frictional force between the block and surface is:
along the surface. If the block is now kept with its face
(a) zero (b) s mg
of smaller area in contact with the surface, the
minimum
force applied parallel to the surface, to set the block in (c) mg
(d) none of these
motion, is
(a) greater than 1.5 N 124. In previous question, if a horizontal
(b) less than 1.5 N force F=umg/2 acts on the block and
m

(c) equal to 1.5 N the block remains stationary, then

(d) may be greater or less than 1.5 N
tension in string is
117. A body of mass 2 kg is at rest on a
(a) zero (b) umg
horizontal table. The 2
coefficient of friction between the body and the table is (c) Amg
2 (d) none of these
0.3. A force of5 N is applied on the body. The
of the body is
acceleration 125. A body of mass 2 kg is placed on a
(a) 0ms2 horizontal surtace
(b) 2.5 ms 2 having kinetic friction 0.4 and static friction 0.5. If the
(c) 5 ms (d) 7.5 ms2 force applied on the body is 2.5 N, then the frictional
force acting on the body will be
 Newton's Laws of Motion 5.13

(a) 8 N (a) F should be cqual to weight of 4 and B

(b) 10 N
(c) 20 N (d) 2.5 N (b) F should be less than weight of 4 and B
In previous question, if the force applied on the
body is (c) F should be more than weight of A and B
20 N, the acceleration of the body will be
(a) 10 ms* (b) 6 ms? (d) System cannot be in equilibrium (at rest).
(c) S ms2
(d) 8.75 ms 134. A block of mass 1kg is at rest on a horizontal table. The
Arectangular body is held at rest by pressing it against a cocfficient of static friction between the block and the
vertical wall for which u < 1. Which of the following is table is 0.5. The magnitude of the force acting upwards at
generally true? an angle of 60° from the horizontal that will just start the
(a) lt will be easier to hold the body if the surfaces in
contact are smooth.
block moving is
20
(b) Pressing force required is smaller than weight mg of (a) SN (b)
the body 2+
(c) Pressing force required is greater than weight ng of 20
(c) (d) 10N
the body 2-/3
(d) The required pressing force is independent of
coefficient of friction between surfaces in contact. 135. Abox of mass mkg is placed on the rear side of an open
128. Ablock of weight Wis held against a vertical wall by truck accelerating at 4 ms. The coefficient of friction
applying a horizontal force of 75 N. The surface of the between the box and the surface below it is 0.4. The net
wall is rough. Now, (consider < 1) acceleration of the box with respect to the truck is zero.
(a) W< 75 N (b) W=75 N The value of m is
(c) W>75 N (d) None of these (a) 4 kg (b) 8 kg
129. A block pressed against the vertical (c) 9.78 kg (d) It could be any value
wall is in equilibrium. The minimum 136. A body of mass 8 kg lies on a rough horizontal table.
coefficient of friction is:
(a) 0.4 mg
It is observed that a certain horizontal force gives the body
m an acceleration of4 ms. When this force is doubled. the
(b) 0.2
(c) 0.5 acceleration of the body is 16 ms The coefficient of
mg
(d) none of these 2 friction is
(a) 0.2 (b) 0.3
130. In previous question, ifu = 0.3, the acceleration of the
block will be: (c) 0.4 (d) 0.8
(a) zero (b) &‘ 137. A body of mass 40 kg resting on a rough horizontal
10 surface is subjected to a force which is just enough to
(c) 84 (d) start the motion of the body. If u, = 0.5 u, -0.4, g= 10
4 5 ms and the force P is continuously applied on the body,
131. A force of 100N is applied on a then the acceleration of the body is
block of mass 3 kg as shown in the (a) zero (b) 1 ms
figure. The coefficient of friction 303kg (c) 2 ms-2 (d) 2.4 ms
between the surface and the block
1 100 N 138. A 3 kg block is pulled by a
is = The frictional force force which is inclined at 37°
3 ka
A37.
to the horizontal table. The
acting on the block is
friction coefficient between the
(a) 15 N downwards (b) 25 N upwards
(c) 20 N downwards table and block is 1/3. For what minimum value of this
(d) 30 N upwards
force, will the block start sliding?
132. In previous problem the acceleration of block is (a) SN (b) 10 N
(a) zero (b) 10 ms upwards (c) 20 N (d) 25 N
(c) 10m/s downward (d) none of these
Wall 139. Ablock of mass m is placed in equilibrium on a moving
133. Figure shows two blocks A and B
pushed against the wall with the force plank. The maximum horizontal acceleration of the plank
F. The wall is smooth but the surfaces EA B for =0.2 is:
in contact of Aand B are rough. Which (a) 2 m/s (b) 3 m/s?
of the following is true for the system (c) dependent on the mass m (d) none of these
of blocks to be at rest against wall?
 5.I4 Physics arrangementshown in the figure (sin 379
147. In the
a
T40. A block of mass m-) ko is placed in cquilibrium on
a 4 m/s.
moving plank accelerating with acceleration 0.2.
Ifcocticient of frietion between plank and block 10
kg

The fictional force acting on the block is: 4 kg

(a) SN (b) 6 N
0.7
(c) zero (d) 4 N
141. A block of mass m- 2 kg is placed in cquilibrium on a
moving plank acoelerating with acceleration a I m/s´. )37
If coctheient of triction bctween plank and block 0.2. friction is up the plane
(a) dircction of force of of friction is Zero
force
The frictional forre acting on the block is: (b) the magnitude of string is 20N
the
(a) 2 N (b) 4 N (c) the tension in friction is 56 N
(d) magnitude of force of
(c) 3 N (d) None of these

142. A block of mass 70 kg is kept on a rough horizontal m =4 kg is

148. A block of mass inclined
surface (u 0.4), Aperson is trying to pull the block by placed over a rough
The
applying a horizontal force, but the block is not moving. plane as shown in figure.
between
The net contact force exerted by the surface on the block coefficient of friction
is F, then: the block and the plane is u= 37
(a) F= 700N (b) F 280 N 0.5.A force F= 1ON is applied
(c) 700NSFS 754 N (d) F= 754 N on the block at an angle of30 , block and wedoe i
143. A block of mass 2 kg rests on arough inclined plane The friction force between the
making an angle of 30° with the horizontal. The coefficient (a) staticin nature in the direction up the plane and
the value 30.2 N
of static friction between the block and the plane is 0.7. (b) static in nature in the direction down
the na
The frictional force on the block is have the value 30.2 N
(a) 10N (b) 7/3 N (c) kinetic in nature in the direction up the plane
have the value 13.5 N
(c) 10x 3N (d) 7 N (d) None of these
144. For the arrangement shown 149. A block of mass m remains stationary on a fixed inc
in the fig. the tension in the plane of inclination 0. If u = coefficient of static frie
the reaction of ground on the block is:
string is [Given: tan (0.8) = m= 1kg
39°). (a) umg cos (b) mg cos 0 /
(a) 6 N u= 0.8 (c) mg sin (d) mg
(b) 6.4 N 150. Find the maximum value of (M/m) in the situation s
(c) 0.4 N 300
(d) zero
in figure so that the system remains at rest. Fnc
coefficient of both the contacts is 4, string is massless
145. A block of mass 4 kg rests on an inclined plane. The pulley is friction less.
inclinationof the plane is gradually increased. It is found m

that when the inclination is 3 in 5 sin = the block

just begins to slide down the plane. The coefficient of

friction between the block and the plane is cos sin
(a) (b)
(a) 0.4 (b) 0.6 sin - u cos sin - ucos 8
(c) 0.8 (d) 0.75
u cos
146. Ablock of mass 'm' is placed on arough inclined plane. (c) (d) sin - ucos b
sin - ucos
When the inclination of the plane is 0, the block just
begins to slide down the plane under its own weight. The 151. A body of mass 10 kg lies on a A B

rough inclined plane of inclination 30 N

minimum force applied parallel to the plane, to move the
block up the plane, is 0= sinin-! 3 with the horizontal.
(a) mg sin (b) 2mg sin 5
(c) mg cos (d) mg tan When a force of 30 N is applied
 Newton's Laws of Motion 5.I5

on the block parallel to and upward the plane, the total 157. A horizontal force, just sufficient to move a body of mass
reaction by the plane on the block is nearly along: 4 kg lying on arough horizontal surface, is applied on
(a) O4 (b) OB it. The coeflicient of static and kinetic friction between
(c) OC (d) OD the body and the surface are 0.8 and 0.6 respectively.
block has
e Asmall mass slides down an inclined plane of inclination If the force continues to act even after the
is
Awith the horizontal. The coefhcient of friction is - o started moving, the acceleration of the block in m/s
Nhere x is the distance through which the mass slides (g10 m/s').
(a) 1/4 (b) 1/2
down and Mo- a constant. Then the specd is maximum (d) 4
after the mass covers a distance of (c) 2
cos sin 9 158. Blocks A and B in the figure
(b) are connccted by a bar of
negligible weight. Mass of
tan 2tan cach block is 170 kg and
c) (d) ,=0.2 and , =0.4, where
u,and , are the coefficients
153. Ablock of mass m, lying of limiting friction between
on a horizontal plane, is blocks and plane, calculate
acted upon by a horizontal 15
the force developed in the
force P and another force
m bar (g = 10 m/sec):
Q. inclined at an angle (a) 150N (b) 75 N
to the vertical. The block (c) 200N (d) 250 N
willremain in equilibrium, if the coefficient of friction
between it and the surface is: 159. A 40 kg slab rests on a frictionless floor as shown in the
(a) (P+Q sin )/(mg+Q cos ) figure. A 10 kg block rests on the top of the slab. The
(b) (P cos 8+ )/mg- sin ) static coefficient of friction between the block and slab is
0.60 while the kinetic friction is 0.40. The 10 kg block is
(c) (P+Q cos /(mg +Qsin )
(d) (P sin - ) - (mg -Qcos ) acted upon by a horizontal force 100 N. If g= 9.8 m/s,
the resulting acceleration of the slab will be
154. The minimum acceleration that a
must be imparted to the cart in
100N A
the figure so that the block A 10 kg
will notfall (given is the coefficient of friction between 40 kg
the surfaces of block and cart) is given by:
(a) ug (b) gu (a) I m/s? (b) 1.5 m/s?
(d) (c) 2 m/s? (d) 6 m/s'
c)
160. A block A with mass 100
155. Aparticle is projected along the line of greatest slope up a kg is resting on another
rough plane inclined at an angle of45° with the horizontal. block B of mass 200 kg. As
Jf the coefficient of friction is 1/2. their retardation is: shown in figure a horizontal
rope tied to a wall holds it.
(a) (b) The coefficient of friction
2V2 between Aand Bis 0.2 while
coefficient of friction between B and the ground is 0.3.
(c) ) (d) The minimum required force F to start moving B willbe
(a) 900 N (5) 100 N
156. A block of mass 15 kg is (c) 1100 N (d) 1200N
resting on arough inclined
plane as shown in figure. The
block is tied by a horizontal Dynamics of Clrcular Motion
string which has a tension 161. An unbanked curve has a radius of 60m. The maximum
of 50 N. The coefficient of 45° speed at which acar can make a turn if the coefficient of
friction between the surfaces
static friction is 0.75, is
of contact is:
(a) 2.1m/s (b) 14 m/s
(a) 1/2 (b) 2/3 (c) 21 m/s (d) 7m/s
(c) 3/4 (d) 1/4
 5.32 Physics

ANSWERKEYS

SECTION A
1. (d) 2. (c) 3. (c) 4. (d) 5. (a) 6. (d) 7. (d) 8. (b) 9. (d) 10.
11. (b) 12. (a) 13. (b) 14. (c) 15. (c) 16. (c) 17. (b) 18. (a) 19. (a) 20.
21. (a) 22. (c) 23. (a) 24. (a) 25. (b) 26. (a) 27. (d) 28. (c) 29. (c) 30,
31. (d) 32. (b) 33. (b) 34. (d) 35. (a) 36. (a) 37. (d) 38. (a) 39. (b) 40.
41. (c) 42. (b) 43. (c) 44. (d) 45. (c) 46. (d) 47. (a) 48. (a) 49. (a)
51. (a) 52. (b) 53. (c) 54. (c) 55. (a) 56. (a) 57. (a) 58. (b) 59. (c)
61. (c) 62. (a) 63. (a) 64. (d) 65.
60. (
(d) 66. (a) 67. (d) 68. (c) 69. (c) 70. (
71. (a) 72. (c) 73. (b) 74. (c) 75. (d) 76. (a) 77. (d) 78. (c) 79. (d) 80.
81. (c) 82. (c) 83. (d) 84. (a) 85. (c) 86. (b) 87. (a) 88. (a) 89. (d)
91. (b) 92. (c)
90.
93. (b) 94. (b) 95. (a) 96. (c) 97. (b) 98. (a) 99. (b) 100.
101. (a
102. (c) 103. (c) 104. (a) 105. (a) 106. (c)
107. (a) 108. (c) 109. (c) 110.
111. (b) 112. (c) 113. (b) 114. (b) 115. (b) 116. (c) 117. (a) 118. (a) 119. (a) 120.
121. (b) 122. (c) 123. (a) 124. (a) 125. (d) 126. (b)
127. (c) 128. (a) 129. (c) 130. (
131. (c) 132. (a) 133. (d) 134. (b) 135. (d) 136. (d) 137. (b) 138. (b) 139. (a) 140,
141. (a) 142. (c) 143. (a) 144. (d) 145. (d) 146. (b) 147. (a) 148. (c) 149. (d) 150.
151. (a) 152. (b) (c) 153. (a) 154. 155. (d) 156. (a) 157. (c) 158. (a) 159. (a) 160. (
161. (c) 162. (a) 163. (c) 164.
(c) 165. (a) 166. (c) 167. (a 168, (b) 169. (a) 170.
171. (a) 172. (d) 173. (d) 174. (d) 175. (a) (
181. (d) 182. (b) 183.
176. (c) 177. (c) 178. (c) 179. (c) 180.
(b) 184. (b) 185. (c) 186. (c) 187. 188.
(a) (c) 189. (d) 190. (0
191. (a) 192. (d) 193. (d) 194. (d)
195. (a) 196. (c) 197. (a) 198. (d) 199. (c) 200.
201. (c) 202. (d) 203. (a 204. (a) 205. (a) 206.
(a
(b) 207. (d) 208. (C) 209. (d) 210.
211. (a) 212. (c) 213. (b) 214. (c) 215. (b) 216. (d) (6)
221. (C) 222. (d) 223.
217. (c) 218. (c) 219. (b) 220. (d
(a 224. (b) 225. (c) 226. (d) 227. (c) 228. (c) 229.
231. (d) 232. (a) 233. (d) 234. (d) 235. (a) 236. (d) (d) 230. (c)

SECTION B
1. (b) 2. (b) 3. (b) 4. (c) 5. (c) 6. (b) 7. (d) 8. (d)
11. (a) 12. (a) 13. (a) 14. (a)1 9. (d) 10. (a)
15. (a)
SECTION C
1. (c) 2. (c) 3. (b) 4. (d) 5. (c)
11. (a) 6. (b) 7. (d) 8. (a)
12. (c) 13. (b) 14. (c) 9. (c) 10. (C)
21. (d) 22.
15. (b) 16. (b) 17. (a)18. (c)19, ()20. (@
(a) 23. (a) 24. (d) 25. (d) 26. (c) 27. (b)
31. (a) 32. (a) 33. (a) 34. (c) 28. (a) 29. (a) 30. (0)
35. (c) 36. (a) 37. (d) 38. (a) 39. (a)
SECTIOND
1. (b) 2. (c) 3. (d) 4. (a) 5. (a) 6. (b) 7. (b)
11. (a) 12. (c) 13. (b) 8. (d) 9. (d) 10. (d)
14. (c) 15. (b) 16. (b) 17. (a)
21. (d) 22. (b) 23. (d) 24. (b) 25. (b) 26. (a)
18. (b) 19. (d) 20. (b}
27. (a) 28. (b) 29. (c) 30. ()