Question

Please solve this question

Answer 1

Answer:

Ok, so we're going to need the concept of gravitational acceleration, a bit of Kinematics and conservation of linear momentum,

The block that's falling down will gain velocity only in the vertical direction while falling down because it is constrained to do so due to the walls on either side.

So, once that it travels the distance h downwards it's velocity at that moment can be calculated as :

v^2 = 2gh

or,

v = √2gh

Now, because this falling mass m and the mass m sliding on the wedge kept on the ceil is connected through the same string then at that very instant the velocity of that block wrt wedge at that instant must also be √2gh.

So, now because there's no external force acting on the considered system, we can conserve linear momentum in the horizontal direction and not in the vertical direction because there's Gravitation force acting on the system.

So, now conserving momentum in horizontal direction.

We get,

Initial moment = 0

Final momentum = m(√2gh-v) - Mv-mv

So,

0 = m(√2gh) - (M+2m)v

or,

v = m(√2gh)/2m+M

So, this will be the velocity of the wedge at that instant

Hope this helps you !