The sphere `A` of mass `m_(1)` moves with velocity `V` on a frictionless horizontal surface and strikes with sphere `B` of mass `m_(2)` at rest. The sphere `A` comes back with speed `V//10`. Choose the correct option.

Options

A. `m_(1) gt m_(2)`
B. `m_(1) = m_(2)`
C. `m_(1) lt m_(2)`
D. none of these

Answer

A

Explanation

`m_(1)V = m_(2)V_(2) - m_(1) (V)/(10)`
`e = 1 = (V_(2) - (-V//10))/(V - 0)`
or `V_(2) + (V)/(10) = V`
From eqn (i), `(m_(1))/(m_(2)) V = V_(2) - (V - m_(1))/(10 m_(2))`
From eqn (ii), `(m_(1))/(m_(2)) V = (V - (V)/(10)) - (V)/(10) (m_(1))/(m_(2))`
or `11 m_(1) = 9m_(2) implies m_(2) gt m_(1)`