A small ball of mass 10 kg is attached at one end of a massless string of length

Question

A small ball of mass 10 kg is attached at one end of a massless string of length 10 m. A person holds the other end of the string. Initially, the ball is going around the person at a tangential speed of 1 m/s on a horizontal frictionless floor. Then, the person pulls in the string so that its length becomes 5 m as the ball continues to rotate.

11. Which of the following statements applies to this simulation?

a. The rotational kinetic energy of the ball is conserved

b. The linear momentum of the ball is conserved

c. The angular momentum of the ball is conserved

12. What is the speed of the ball after the length of the string was shortened to 5 m?

a. 0.5 m/s

b. 1 m/s

c. 2 m/s

d. 4 m/s

e. 8 m/s

Explanation / Answer

11. force that pulling ball is along the rope.

hence torque due to that force will be zero.
torque = r x F = r F sin(theta )

theta = 0 -=> torque = 0

So, angular momentum will be conserved.

Ans(c)

12. angular momentum = I w

Ii wi = If wf

m vi ri = m vf rf

1 x 10 = vf x 5

vf = 2 m/s

Ans(c)

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