The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest,
A)the block at the left lands first.
B)the block at the right lands first.
C)both blocks land at the same time.

Question

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest, 
A)the block at the left lands first. 
B)the block at the right lands first. 
C)both blocks land at the same time.

Quizplus · Accepted Answer

The time period of a simple pendulum is given by T= 2π√(l/g), where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.

For the system on the left, the effective length of the pendulum is r, as the bob moves in a circular path of radius r. 
For the system on the right, the effective length of the pendulum is r/2.

We know that the time period of the pendulum increases as its length increases. Therefore, the pendulum on the left would have a longer time period than the pendulum on the right, and consequently, take longer to complete one oscillation.

Since both pendulums start from rest, the pendulum on the right would complete its first oscillation faster and the block attached to it would touch the ground first. Therefore, the answer is B.

The Rotating Systems Shown in the Figure Differ Only in That