In the Fig. shown, mass 'm' is being pulled on the incline of a wedge of mass M. All the surface are smooth. Find the acceleration of the wedge.

Explanation

Free diagram of wedge .

Then by Newton 's 2nd law from above diagram
` N sin theta = M"" A ` …….(i)
Free body diagram of block .

Now, by Newton's 2nd law from above diagram along the x- axis
` mA cos theta + mg sin theta = ma_(1)" " ` ....... (ii)
Along the y - axis , ` N + mA sin theta = mg cos theta " " ` ......(iii)
From eq. (i) & (ii)
` (MA)/(sin theta ) + mA sin theta = mg cos theta `
` A = (mg sin theta cos theta )/(M + m sin ^(2)theta)`