Correct Answer - A
`m_(1)g-N_(1)=m_(1)a_(1)` ….(i)
`(N_(1)+m_(2)g)sin theta=m_(2)a_(2)` ….(ii)
From (i) and (ii)
`[(m_(1)g-m_(1)a_(1))+m_(2)g]sin theta=m_(2)a_(2)`
`(m_(1)+m_(2))g sin theta-m_(1)a_(1)sin theta=m_(2)a_(2)` ....(iii)
Block `m_(1)` can move only in vertical direction as there is no force in horizontal direction. Since acceleration along normal at point of contact of the block and wedge should be equal.
So, `a_(1)=a_(2) sin theta` ...(iv)