Two bodies of masses `m_(1)` and `m_(2)` are attached to the two ends of a string. The passes over a pulley of mass m and radius R. if `m_(1)gtm_(2)` . The acceleration the system will be

Options

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

Answer

C

Explanation

`m_(1)g-T_(1)=m_(1)a`
`T_(2)-m_(2)g=m_(2)a" "....(ii)`
`:. (T_(1)-T_(2))+(m_(1)+m_(2))a=(m_(1)-m_(2))g`
`rArrT_(1)-T_(2)=(m_(1)-m_(2))g-(m_(1)+m_(2))a`
`" " tau=(T_(1)-T_(2))R=Ialpha`
`" " =(1//2)mR^(2)(a//R)" " ....(iii)`
`rArr(T_(1)-T_(2))=(1//2)ma" " ....(iv)`
From (iii) and (iv)
`" " (1//2)ma=(m_(1)-m_(2))g-(m_(1)+m_(2))a`
`rArr a=(m_(1)-m_(2))/(m_(1)+m_(2)+(m//2))g`