Figure shows a small block of mass m which is started with a speed v on the horizontal part of the bigger block of mass M placed on a horizontal floor. The curved part of the surface shown in semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

#### Solution

The mass of the small block is m.

Initial speed of this block is v.

The mass of the bigger block is M.

Initial speed of this block is zero.

At point A, as the small block transfers its momentum to the bigger block, both the blocks move with a common velocity V (say) in the same direction as v.

Using the law of conservation of linear momentum, we can write:

Initial momentum = final momentum

MV + M × O = ( m +M)V

⇒ V = `(mv)/(m + M)`

Therefore, the speed of the bigger block when the smaller block reaches point *A* of the surface is `(mv)/(m + M)`.