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,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively,then A)t_L t_R. B)t_L = t_R. C)t_L

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,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively,then A)t_L > t_R. B)t_L = t_R. C)t_L < t_R.

Quizplus · Accepted Answer

The time taken for a block to reach the bottom of a pendulum of length L is given by T=2π√(L/g), where g is the acceleration due to gravity. In this case, the length of the pendulum is the distance from the axis of rotation to the center of mass of the block. Therefore, for the pendulum on the left, the length is r and for the pendulum on the right, the length is r/2. As T is proportional to √L, it follows that t_L > t_R.

The Rotating Systems Shown in the Figure Differ Only in That