In the arrangement shown, the pulleys are fixed and ideal, the strings are light, `m_(1)gtm_(2)` and S is a spring balance which is itself massless. The readings of S (in units of mass) is

Options

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

Answer

D

Explanation

Reading of spring balance = T
`T = (2m_(1) m_(2))/(m_(1) + m_(2)) gN`
Mass `= (2m_(1)m_(2))/(m_(1) + m_(2))`