In the figure, pulleys are smooth and strings are massless, `m_(1)`=1 kg and `m_(2)=(1)/(3)`kg. To keep `m_(3)` at rest, mass `m_(3)` should be

Options

A. 1 kg
B. `(2)/(3)kg`
C. `(1)/(4) kg`
D. `2 kg`

Answer

A

Explanation

(a) `m_(3)` is at rest, Therefore

2T`=m_(3)g`….(i)
Further if `m_(3)` is at rest, then pully P is also at rest. Writing equations of motion.
`m_(1)g-T=m_(1)a` ….(ii)
`T-m_(2)g=m_(2)a` ...(iii)
Solving Eq. (ii) and (iii) we get, `m_(3)=1 kg `