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. On removing the clamp, `m_(1)` and `m_(2)` start moving. How much change in counter mass has to be made to restore balance ?

Options

A. `g(m_(1)-m_(2))^(2)/((m_(1)+m_(2))` to be reduced
B. `g(m_(1)-m_(2))^(2)/((m_(1)+m_(2))` to be increased
C. `g(m_(1)-m_(2))/((m_(1)+m_(2))`to be increased
D. `g(m_(1)-m_(2))/((m_(1)+m_(2))`to be increased

Explanation

When `m_(1)` & `m_(2)` not moving
Then `W_(1)= (m_(1)+m_(2))g`
When `m_(1) & `m_(2)` are moving W_(2) `=(4m_(1)m_(2)g)/(m_(1)+m_(2))`
`:.` Reduced wt`=W_(1)-W_(2)`