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11th Physics Monthly Test - 2 ( Motion of System of Particles and Rigid Bodies )

MABS Institution

11th Physics Monthly Test - 2 ( Motion of System of Particles and Rigid Bodies )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms^-1 relative to the ground. Time taken by the man to complete one revolution is

\(\pi s\)
\({3\pi\over 2} s\)
\(2\pi s\)
\({\pi\over 2} s\)

Two discs of same material have the same mass. If their thicknesses are in the ratio 1:3, then their moments of inertia are in the ratio

3:1
1:3
1:9
\(1:\sqrt{3}\)

Where will be the centre of mass on combining two masses m and M (M > m)?

Towards m
Towards M
Between m & M
away from m & M

lf the linear momentum and angular momentum are zero, then the object is said to be in

stable equilibrium
unstable equilibrium
neutral equilibrium
all the above

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

M.I
Angular momentum
Angular velocity
Rotational K.E.

If a gymnast sitting on a rotating stool, with his arms out stretched, suddenly lowers his hands:

the angular velocity decreases
his moment of Inertia decreases
the angular velocity stays constant
the angular momentum increases

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia,

Rotational kinetic energy is given by

\(\frac { 1 }{ 2 } \)mv²
\(\frac { 1 }{ 2 } \)Iv²
\(\frac { { L }^{ 2 } }{ 2I } \)
\(\frac { 2I }{ L^{ 2 } } \).

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

2v
Zero
1.5v
v

Two particles P and Q move towards with each other from rest with the velocities of 10 ms^-1 and 20 ms^-1 under the mutual force of attraction. The velocity of centre of mass is

15 ms^-1
20 ms^-1
30 ms^-1
zero

Part - B

Generic 2 - Answer All Question

Two solid spheres of the same mass are made of metals of different densities. Which of them has a large moment of inertia about the diameter?

When does the body have precession?

State law of Conservation of angular momentum.

Why there are two propellers in a helicopter?
If no external torque acts on a body, will its angular velocity remain conserved?

When an angular momentum of the object will be zero?

A particle moves in a circular path with decreasing speed. What happens to its angular momentum?

Part - C

Generic 3 - Answer All Question

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm, what is the mass of the meter stick?

A cyclist while negotiating a circular path with speed 20 m s^-1 is found to bend an angle by 30° with vertical. What is the radius of the circular path? (given, g = 10m s^-2)

When does a rigid body said to be in equilibrium? State the necessary condition for a body to be in equilibrium.

A rolling wheel has velocity of its center of mass as 5 m s^-1. If its radius is 1.5 m and angular velocity is 3 rad s^-1 , then check whether it is in pure rolling or not.

List the condition on which angular momentum is zero.
If the force applied is perpendicular to the handle of the spanner as shown in the diagram, find the (i) torque exerted by the force about the center of the nut, (ii) direction of torque and (iii) type of rotation caused by the torque about the nut.

Find the values of torque for different cases.

Part - D

Generic 5 - Answer All Question

Explain the types of equilibrium with suitable examples:

Derive the expression for moment of lnertla of a uniform ring about an axis passing through the center and perpendicular to the plane

A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases from 20\(\pi\) rad/s to 40\(\pi\)rad/s in 10 seconds. Find the number of rotations in that period.

State in the absence of any external force the velocity of the centre of mass remains constant.

Derive an expression for the Center of Mass of Two Point Masses.

Define Torque and derive its expression.

State and prove perpendicular axis theorem.

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