(Solved): A merry-go-round of radius R, shown in the figure, is rotating at constant angular speed. The fricti ...

A merry-go-round of radius R, shown in the figure, is rotating at constant angular speed. The friction in its bearings is so small that it can be ignored. A sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. The sandbag does not slip or roll upon contact with the merry-go-round. Rank, from greatest to least, the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag ”sticks” to the merry-go-round. Make sure to list other quantities that are assumed to be given in your solution.

A. m_A = m and r_A = 1/2 R

B. m_B = m and r_B = 1/4 R
C. m_C = 2m and r_C = 1/4 R

D. m_D = 3/2 m and r_D = 3/4 R
E. m_E = m and r_E = R