This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Angular Momentum”.

1. A child sits stationary at one end of a long trolley moving uniformly with speed v on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, then what is the effect of the speed of the centre of mass of the (trolley+child) system?

a) The speed of the centre of mass increases

b) The speed of the centre of mass decreases

c) The speed of the centre of mass will not change

d) The speed of the centre of mass will first increase and then decrease

View Answer

Explanation: The force involved in the given problem is the internal forces of the system. No external force acts on the system when the child runs So, there will be no change in the speed of the centre of mass of the (trolley+child) system.

2. A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will reach the bottom _____________

a) With the same speed

b) With different speed

c) With different speed but same time

d) Immediately

View Answer

Explanation: Acceleration of the rolling sphere,

a=gsinθ/((1+k

^{2}/R

^{2}))

Velocity of the sphere at the bottom of the inclined plane,

v=√(2gh/((1+k

^{2}/R

^{2})))

The sphere will reach the bottom with the same speed v because h is the same in both the cases.

3. A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will _____________

a) Reach the bottom at the same time

b) Will take longer time to roll down one plane

c) Reach the bottom at an unpredictable time

d) Reach the bottom at the same time and keeps rolling

View Answer

Explanation: Acceleration of the rolling sphere,

a=gsinθ/((1+k

^{2}/R

^{2}))

Velocity of the sphere at the bottom of the inclined plane,

v=√(2gh/((1+k

^{2}/R

^{2})))

The sphere will take a longer time to roll down one plane than the other. It will take a larger time in case if the plane with smaller inclination because the acceleration is proportional to sinθ.

4. A hook of radius 2m weighs 100kg. It rolls along a horizontal floor so that its centre if mass has a speed of 20cm/s. How much work has to be done to stop it?

a) 5 J

b) 6 J

c) 2 J

d) 4 J

View Answer

Explanation: v

_{cm}=20cm/s = 0.20ms

Work required to stop the hoop = Rotational kinetic energy+Traslational kinetic energy

Work required = \(\frac{1}{2} Iω^2+\frac{1}{2} Mv_{cm}^2 = 4J\).

5. During rolling, the force of friction acts in the same direction as the direction of motion of the centre of mass of the body.

a) True

b) False

View Answer

Explanation: When a body rolls, the force if the friction acts in the same direction as the direction of motion of the centre of mass of the body.

6. Where does the centre of mass of two particles of an equal mass lie?

a) Inside the body

b) Outside the body

c) Near the first body

d) Midway between them

View Answer

Explanation: The centre of mass of two particles of equal masses lies midway between them. Its position vector is the average of the position vectors of the two particles.

7. Two particles A and B, initially at rest, move towards each other under mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, what is the speed of mass of the system?

a) 3v

b) v

c) Zero

d) 1.5v

View Answer

Explanation: No external force is acting on the centre of mass. It remains at rest. The speed of centre of mass is zero.

8. A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and the centre of mass velocity u. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ω_{(A)} and ω_{(B)} respectively. Then?

a) ω_{A} is lesser than ω_{B}

b) ω_{A}=ω_{B}

c) ω_{A}=ω

d) ω_{B}=ω

View Answer

Explanation: Only their linear velocities are exchanged. The two spheres cannot exert torques on each other, as their surfaces are frictionless, and so that angular velocities of the sphere do not change.

9. Moment of inertia of a circular wire of mass M and radius R about its diameter is _____________

a) 1/2 MR^{2}

b) 1/4 MR^{2}

c) 2MR^{2}

d) MR^{2}

View Answer

Explanation: A circular wire behaves like a ring. By perpendicular axes theorem,

I

_{D}+I

_{D}=1/2 MR

^{2}

Therefore,

1/4 MR

^{2}.

10. One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively I_{A} and I_{B}, such that _____________

a) I_{A}=I_{B}

b) I_{A} is greater thab I_{B}

c) I_{A} is lesser than I_{B}

d) I_{A}/I_{B} =ρ_{A}/ρ_{B}

View Answer

Explanation: In a hollow sphere, the mass is distributed away from the axis of rotation. So, its moment of inertia is greater than that of a solid sphere.

**Sanfoundry Global Education & Learning Series – Engineering Physics.**

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