The mass of wedge, shown in figure is M and that of the block is m. Neglecting friction at all the places and mass of the pulley. Calculate the acceleration of wedge. Thread is inextensible.

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)`