Find the acceleration of the body of mass `m_(2)` in the arrangement shown in figure. If the mass`m_(2)` is `eta` time great as the mass `m_(1)` and the angle that the inclined plane forms with the horizontal is equal to `theta`. The masses of the pulley and threads, as well as the friction, are assumed to be negligible.

Options

A. `(2g(2eta-sin theta))/(2eta+1)`
B. `(2g(2eta-sin theta))/(4eta+1)`
C. `(2g(2eta-sin theta))/(3eta+1)`
D. `(4g(2eta-sin theta))/(3eta+1)`

Answer

B

Explanation

`Ta_(2)-2Ta_(1)=0, a_(2)=2a_(1)`......(i)
`m_(2)g-T=m_(2)a_(2)`.....(ii)
`2T-m_(1)g sin theta=m_(1)a_(1)`....(iii)
Solving three equations, `a_(2)=(2g(2eta-sintheta))/(4eta+1)`