The figure shows a small block of mass m which is given a velocity v on the horizontal part of a bigger block of mass M slides on the bigger block,all the surfaces are frictionless and the curved part is semicircular,
the question asks to find the velocity of the bigger block when the smaller block reaches the point A.
the solution to the question is as follows,
as there is no external force in the horizontal direction, the linear momentum of the system will be conserved along the horizontal direction,
At the point A the net velocity of the smaller block wirh respect to the bigger block is only upward,
so its horizontal relative velocity wrt the bigger block is 0, so both blocks move to the left with the same velocity v',
so $$m v = ( m v' + M v') = ( m + M ) v'$$
$$v' = mv/(m + M )$$
this solves the problem, my concern is,
for any other point in the curve,for the blocks to be in contact,will the horizontal velocities of both blocks be the same ?
Will the process and answer remain the same for any other point in the curved path or it will change,if it changes how will it change.
this is the question number 29 of chapter 9 from the book "concepts of physics" by h.c verma from the section center of mass,linear momentum and collision.