Super-30 LAKSHAY 90` CLASSES
Assignment
Physics XI Circular Motion Date: 25/10/2023
1. ADarticle of wass » slides on the inner surface of a
smooth cone of apex 2g figure I). If the particle moves
in a horizontal circle with speed u at a height h block ?
above the vertex, then find h.
Fig. 3
2a mg | mg
mor
Fig. I (a) (b)
(a) tan cot
(b) |mg mg
2g
(c)
mo r
(d)
mo
(c) tan 0 (d)
2. Aparticle of mass M rotates in a circle of radius 4. A carnival rotor ride has a person standing on a
rwith a uniform angular speed o. This particle is ledge inside a large cylinder that rotates about a
observed from arefrence frame that rotates about vertical axis. When it reaches the high enough
-axis with a constant angular speed o, (figure angular speed, the ledge drops away. If the speed
2). What centrifugal force (pseudo force) would of rotation and the radius of the cylinder be o
act on the particle ? and R respectively. then what is the minimum
coefficient of friction u for the person not to
slide down ?
()
reference Particle's Motion
frame
Fig. 2
Fig. 4
(a) Mo`r (b) Mo,r
(a) (b
()
(c) (d)
2 8
(c) (d)
disc that 2or
A block of mass m rests on a rough
()
3.
an axis
rotates with an angular speed of o about 5. A bucket half filled with water is whirld in vertical
perpendicular to
passing through its centre and circle with a massless and inextensible rope attached
distance of the block fron the to it (igure S) The water does not spill out even
its plane. The motion of block
rotation axis is r (figure 3). The when the bucket is inverted at the top of its path.
standing on the ground. See the following
Is observed by a person satenent:
friction between the
Hj represents the force of
biock and the dise. then which ol the following
body diagram of the
correctly represents the free
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No.:
Phone 9891214179, 011-40154386
ooth .
o0 lop of
). A Drtiele rests possible onotal ,
dius Wht least
further COL
without Wakinp
(he sphere
the sphere (tigure 0)
Fig. 5
JA] Weight of' the water is less than the centriipetal
force needed to rotate it in a circular path.
IBI Water passes througn a state 0f weightlessness
when atthe top of the motion.
(a) A is correct. B is
Wrong
() V (b) /2
is correct (d) /r/2
(b) A is wrong, B (c) 2/r
Wrong
(c) Both A and B are 10. Which of the followine is a
false statement ?
Bare correct uniformly in a circle is i
(d) Both A and
(a) A particle novine
on a level circular
Acar of mass m is mOving rotational cquilibrium.
instant its linear a circular motion. The
6.
road of radius r. At a particular constant rate a. (b) A particle is excutinp
that acts on the
speed is that increases at the moment of centripctal force
of the particle
See the following
statements: particle about the axis of rotation
tyres of car
[AIThe friction coefficient between
is zero.
the direcction ol
and the road is greater than a/g. (c) A force cannot determine dircction of
frictional force between motion but can determine the
[B] The magnitude of the greater than acceleration.
is
the tyres of car and the road uniformly in a
(d) Velocity of a particle moving
circle is constant.
statement ?
11. Which of the following is a false
(a) A is correct, B is wrong equally rough circular
correct (a) A snmall body slides along I and 2 of
(b) A is wrong. B is surfaces from A to B via route
represcnt
(c) Both A and B are wrong cqual radius (figure A). Ifv, and v, B
on reachin
(d) Both A and B are correct the velocities of the body
somekind of motion in a along the paths I and 2respectively then v,
7 A particle executes normal
the
horizontal plane. Let a, and a, represent particle as
> V,.
of the
and the tangential acceleration
statements:
it moves. See the following
[A] 4,, 0 but a, 0 implies that the particle
motion.
executes non-uniform rectilinear
particle
|B]a, * 0 but a, = 0 implies that the
B
Fig. A
executes uniform circular motion. a car within the
givCn
stop
(b) It is easicr to rather
(a) A is correct, B is wrong distance, say d by applying brakes
turn (figure B).
(b) A is wrong, B is correct than by taking circular
(c) Both A and B are wrong
(d) Both A and B are corrcct
8. Fig. B
A motor car moves on a circular level road of of radius
particle is executing circular motion
radius 30/3 m with a constant specd o! (c) A acceleration of the
with speed v. The net
R circle,
10/3 m/s. A metal bob is suspended from ceiling towards centre of
particle is always acceleration
of the car by a light thread of length I m. represent the normal
angle does the thread make with the road ?What (d) Ifa, and a,
acceleration of the partiele
(a) 300
and the tangential respectively then
(b) 60° in circular motion
(c) 450 ()
(d) 75°
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Phone No. : 9891214179, 0[-40154386
circular
motion of
.particle of mass n excutes a H,=0.3, determine the time required to cause him
(figure 7), what
dius R uniformiy with speed vforce that aetc to slip.
the average
is the modulus of
distance equal to quater of a
the particle over a
circle ?
R
Fig. 10
(a) 4.5 s (b) 5.5 s
Fig. 7 (c) 6.5 s (d) 7.5s
2V2my' 4V2my? 16. T'wo bobs of equal mass are attached to an
(b)
(a)
TR TR Inextensible and massless string of length Im
V2my? (tigure 11). The string is whirled in a horizontal
4
2/3my? (d) circle about O at a constant rate. If T and T
(c) PO of
TR IR represent the tension in the part PQ and
A coin C at a distance 4 cm from the axis of a ratio
the string respectively than what is the
13.
T
turn table just flies off when the speed of rotation
of turntable in o (figure 8). At what distance
from the axis of rotation would the same coin fly P
off if speed of rotation of the turntable is doubled ?
Fig. 8
(a) 0.5 cm (b) 2 cm
OP = PQ = Im
(c) 8 cm (d) I cim Fig. 11
end of a massless
14. A 3kg disc D is attached to the end of
andinextensible cord (figure 9). The other (a) 3
the ball and socket joint
the cord is attached to platform 3
The
located at the centre C ofaplatform. on it and (c) (d) I
the disc is kept 2
is rotating rapidly and the time ittakes for the
released from rest. Find the 17. A simple pendulum is vibrating with an angular
great enough to break amplitude of r/2. For what value of a the resultant
disc to reach a speed cord can sustain
tension the acceleration is directed horizontally (figure 12) ?
cord. The maximum
coefficient of friction between
is 300 N and the
is u, = 0.1.
disc and the platform
Motion
Fig. 9
(b) 10s Fig. 12
(a) 5s
(d) 20.
(c) 15s (a) (b) 180°
sits 3 m from
has a mass of 80 kg and
The man (figure 10)
15.
center of the rotating platform from (c) cos
the increased (d) cos
to the rotation his speed is J3
Due static
coefficient of
rest by =0.4 m/s. If the platform is
clothes and the
friction between his
School, Sector-22, Dwarka-1 10077
F-IManish (GlobalMall, Opposite Mt. Carmel 011-40154386
Phone No. : 9891214179,
that
l0 N. of this
so 700seat
a,. at
n, acceleration
800 thetraveling
weighs
on
m/s m/s
260 280
(d)
? 6.7
p man exerts point(b)
kN 4.7
kN
(d)
curvature is
maximum (b) thehe plane
lowest
14
Fig. if force
800m
p= 19, the
of the
when
normal
aexperiences
radius question
at
(fligure
14). (a)
250
m/s (c)
plane
is
270
m/s the and (a)
a kN 5.7
7.7 (c)
kN
having to is air
Refer
What speed
he the
20.
radius
to speed friction
cartons which
curve
required
0.8.
constant
smallest at vertical
that
static= speed
are ,
so
kg ata the of is
conveyor (b) 8m/s constant
6m/s (d) the
Determine conveyor
coefficients
5 line around
of
assembly
mass maximum
the and Fig.
13
l3).for travel
a Thecarton
having
the(figure
p,
thecan
along curvature,
slip.
Determine
a 7m/s (c)
(a) 5m/s
Cartonsm/s not between pilot
move
8 the
of of do 8m/s
18. 19.
