Two wires are arranged as shown in the figure. The elongation in upper and lower wire are respectively

Options

A. `((m_(1) + m_(2)) gl_(1))/(AY_(1)), (m_(2) gl_(2))/(AY_(2))`
B. `((m_(1) - m_(2)) gl_(1))/(AY_(1)), (m_(2) gl_(2))/(AY_(2))`
C. `(((m_(1))/(m_(2)) + 1 ) gl_(1))/(AY_(1)), (m_(2) gl_(2))/(AY_(2))`
D. `(((m_(1))/(m_(2)) - 1 ) gl_(1))/(AY_(1)), (m_(2) gl_(2))/(AY_(2))`

Answer

A

Explanation

For lower wire `F = m_(2)g`
`F = (F l_(2))/(A Y_(2)) rArr e_(2) = (m_(2) g l_(2))/(AY_(2))`
For upper wire `F = (m_(1) + m_(2))g`
`e_(1) = (F l_(1))/(AY_(1)) = ((m_(1) + m_(2))gl_(1))/(AU_(1))`