Question

A ball is moving towards the wall as shown in the diagram then momentum is conserved

1) along the wall

2) along the perpendicular to the wall

3) along any direction

4)both (1) & (2)

Answer 1

the answer should be (4).
The product of mass times velocity is defined as momentum or linear momentum.
The rate of change of linear momentum of a body with tome is proportional to the net force(Newton's 2nd law).
When we break or resolve the given direction of force(arrow part), it'll be giving two forces fx & fy along x & y axes respectively.
Since, F is mdv/dt or simply dp/dt, so momentum will be conserved & taken in account in the direction perpendicular to the wall (x axis) & along the wall(y axis).
Hope this helps!
Feel free to ask your doubts!!:-D

Answer 2

Resolving the initial velocity into components, mvsinθ (along y i.e the wall) and mvcosθ (along x i.e perpendicular). Similarly the final velocity is resolved into mvsinθ (along y i.e the wall) and mvcosθ (along x i.e perpendicular).

Now, change in momentum along the perpendicualr = Pf - Pi

= -mvcosθ - mvcosθ

= -2mvcosθ

Change in momentum along the wall

=Pf - Pi

= -mvsinθ - (-mvsinθ)

=0

Thus change in momentum along the wall is zero which means that the momentum is conserved. So answer is one