In the figure shown blocks A and B are kept on a wedge C. A, B and C each have mass m. All, surfaces are smooth. Find the acceleration of C.

Let c be acceleration of wedge C.
a be acceleration of block A w.r.t. wedge C.
b be acceleration of block. B w.r.t. wedge C.
Applying Newton's law in horizontal direction to system of A+B+C.

$mc+m\left(c-a\cos {37}^{\circ }\right)+m\left(c+b\cos {53}^{\circ }\right)=0$    ……(1)

Applying Newton's law to block A and B along the incline gives.

$\text{ In case of }A:mg\sin {37}^{\circ }=m\left(a-c\cos {37}^{\circ }\right)$   …..(2)

$\text{ In case of }B:mg\sin {53}^{\circ }=m\left(b+c\cos {53}^{\circ }\right)$   …..(3)

Solving (1), (2), and (3), we get c = 0