Two weights `w_(1)` and `w_(2)` are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration g , the tension in the string will be

Options

A. `(4w_(1)w_(2))/(w_(1)+w_(2))`
B. `(2w_(1)w_(2))/(w_(1)+w_(2))`
C. `(w_(1)-w_(2))/(w_(1)+w_(2))`
D. `(w_(1)w_(2))/(2(w_(1)+w_(2)))`

Answer

A

Explanation

(a) Writing equation of motion for two weight

`w_(1)-T=(w_(1))/(g)(a_(r)-a)`……(i)
`T-w_(2)=(w_(2))/(g)(ar+a)`……(ii)
Solving Eq.(i) and (ii) we get
`T=(4w_(1)w_(2))/(w_(1)+w_(2))` with a=g