A pulley is attached to one arm of a balance and a string passed around it carries two masses `m_(1)` and `m_(2)`. The pulley is provided with a clamp due to which `m_(1)` and `m_(2)` do not move and the balance is in equilibrium. On removing the clamp `m_(1)` and `m_(2)` start moving with respect to pulley. The counterweight reduced or increased to restore balance is:

Options

A. `(m_(1)^(2)g)/(m_(1)+m_(2))`
B. `((m_(1)+m_(2))^(2)g)/(m_(1)+m_(2))`
C. `(m_(2)^(2)g)/((m_(1)+m_(2))^(2))`
D. zero

Answer

B

Explanation

When theh clamp is removed, the pull on the left arm is `(4m_(1)m_(2)g)/(m_(1)+m_(2))`
When `m_(1)` and `m_(2)` do not move, the pull is `(m_(1)+m_(2))g`
`DeltaW=((m_(1)-m_(2))^(2))/(m_(1)-m_(2))`