Consider a large block placed on a smooth horizontal surface, with a man standing at one end of the block. The man walks to the other end, relative to the block. The distances (absolute) moved by the man and the block are :

Options

A. In the inverse ratio masses
B. In the direction ratio of their masses
C. Independent of their masses
D. Dependent both on their masses and speeds.

Answer

A

Explanation

(a) Let `m` and `M` be the respective masses of the person and the block, and let `l` be its length. Now, if `x_1` and `x_2` be the absolute displacement of the person and the block and `vec x` that of the centre of mass, then
`overline x = (m x_1 + m x_2)/(m + M)rArr Delta overline x = (m Delta x_1 + m Delta x_2)/(m + M)`
Since horizontal forces are absent, so `Delta overline x = 0`
`m Delta x_1 + M Delta x_2 = 0 rArr m(-l) +(m + M) Delta x_2 = 0`
`Delta x_2 = (ml)/(m + M)`
Similarly, `Delta x_1 = (M l)/(m + M)`.
.