A really good problem(Not for everyone)

[FedEx]

A really good problem

Hi
A prism of mass M is kept on a horizontal surface having the inclination of alpha. A small block of mass m is kept on the prism. This block is attached to a vertical wall with a massless rope passing over a pulley which is at the free vertex of the prism.Find the acc of the prism wrt to the block m and wrt the ground.
I hope that you people are able to understand the question.As i am not able to upload the figure.

All the surfaces are friction less. Now what i have been trying is that that the acc with which the block m comes down is equal to the acc with which the prism moves towards the wall because the string is unelastic. But here the acc of the prism is wrt to ground and the acc of the block is wrt to the prism so by triangle law of addition the resultant of these two vectors would be acc of block wrt to the ground. So here we can get the value of the acc of the block wrt ground in terms of the acc of either the prism wrt to ground or the acc of the block wrt prism ,as both are same.

Now there is some tension in the string and this tension opposes the motion of the block on the prism but the block tends to move due to mgsin(alpha). But this tension helps the prism to move towards the wall.Moreover we will have to consider the normal force exerted by the block on prism which will also help the prism to move.But i think we will have to again take a comp of N.Also we will have to consider the normal force exerted by the prism on the block.
I think i have included all the forces,are any forces left to include? If no then i think that the equations which i have formed are correct.I would try to post the equations if i my above logic is approved by you people.

 

[member 553083]

Now i think that the calculation part needs to be done and the resultant acc of block wrt to the ground should be found out. Please suggest the changes if any in my logic and help me with the calculation.