Systems of Particles and Rotational Motion Test

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Systems of Particles and Rotational Motion Test - 60

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Question 1
4 / -1

A solid cylinder is rolling down on an inclined plane of angle θ. The coefficient of static friction between the plane and cylinder is µ_s. The condition for the cylinder not to slip is

A
tan θ ≥ 3 µ

B
tan θ > 3 µ_s

C
tan θ ≤ µ_s

D
tan θ < 3 µ_s

Solution
Question 2
4 / -1

A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved.

A
Centre of the circle

B
On the circumference of the circle

C
Inside the circle

D
Outside the circle
Question 3
4 / -1

Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends, what would be its angular velocity?

A
V /L

B
2V /L

C
V /3L

D
V /4L

Solution
Question 4
4 / -1

A straight rod of length L has one of its ends at the origin and the other at x = L. If the mass per unit length of the rod is given by Ax where A is constant, where is its mass centre?

A
L/3

B
L/2

C
2L/3

D
3L/4

Solution
Question 5
4 / -1

A mass m is moving with a constant velocity along a line parallel to x-axis. Its angular momentum with respect to origin or z-axis is

A
Zero

B
Remains constant

C
Goes on increasing

D
Goes on decreasing

Solution
Question 6
4 / -1

An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

A
Angular velocity and total energy (kinetic and potential)

B
Total angular momentum and total energy

C
Angular velocity and moment of inertia about the axis of rotation

D
Total angular momentum and moment of inertia about the axis of rotation
Question 7
4 / -1

A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

A

B

C

D
Zero

Solution
Question 8
4 / -1

A disc of mass M and radius R is rolling with angular speed ω on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

A

B

C

D

Solution
Question 9
4 / -1

A child is standing with folded hands at the centre of a platform rotating about its centreal axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

A
2K

B
K/2

C
K/4

D
4K

Solution
Question 10
4 / -1

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are

A
Up the incline while ascending and down the incline while descending

B
Up the incline while ascending as well as descending

C
Down the incline while ascending and up the incline with descending

D
Down the incline while ascending as well as descending

Solution