Question

A block of mass m is placed on a triangular block of mass M, which in turn is placed on  horizontal surface as shown in figure (9-E21). Assuming frictionless surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.

Answer 1

The block ‘m’ will slide down the inclined plane of mass M with acceleration a₁ g sin α (relative) to the inclined plane. The horizontal component of a1 will be, a_x = g sin α cos α, for which the block M will accelerate towards left. Let, the acceleration be a₂. According to the concept of centre of mass, (in the horizontal direction external force is zero). ma_x = (M + m) a₂

So, the absolute (Resultant) acceleration of ‘m’ on the block ‘M’ along the direction of the incline will be,