Let's analyze the given situation step by step to find the maximum height attained by block B on wedge C.


When block B is released from the top of wedge A, it will start moving down due to gravity. As there is no friction, the block will slide down without any resistance. The force acting on block B is its weight (mg) and the normal force (N) exerted by wedge A.

Since the block is in contact with the wedge, the normal force can be resolved into two components:
1. Normal force perpendicular to the incline (Nsinθ), where θ is the angle of the incline.
2. Normal force parallel to the incline (Ncosθ), which cancels out the weight of block B.

Therefore, the net force acting on block B is (mg - Ncosθ), which causes the acceleration of the block.


Using Newton's second law (F = ma), we can write the equation of motion for block B on wedge A:
mg - Ncosθ = ma.

Since the wedge is smooth, the normal force can be expressed as:
N = mgcosθ.

Substituting this value into the equation of motion, we get:
mg - (mgcosθ)cosθ = ma.


To find the maximum height attained by block B on wedge A, we need to consider the point where the block comes to rest. At this point, the acceleration (a) becomes zero.

Setting the acceleration to zero in the equation of motion, we get:
mg - (mgcosθ)cosθ = 0.

Simplifying this equation, we have:
mg = (mgcosθ)cosθ.

Canceling out 'mg' from both sides, we get:
1 = cos²θ.

Taking the square root of both sides, we get:
cosθ = ±1.

Since the angle θ cannot be greater than 90 degrees, we take the positive value:
cosθ = 1.

Therefore, θ = 0 degrees, which means the wedge A is horizontal.


When block B ascends another smooth wedge C, the situation is similar to the previous step. The only difference is that the angle of the incline is now 180 degrees (opposite direction).

Using the same equations of motion as before, we can find the maximum height attained by block B on wedge C.

Setting the acceleration to zero in the equation of motion, we get:
mg + (mgcosθ)cosθ = 0.

Simplifying this equation, we have:
mg = -(mgcosθ)cosθ.

Canceling out 'mg' from both sides, we get:
-1 = cos²θ.

Taking the square root of both sides, we get:
cosθ = ±1.

Since the angle θ cannot be greater than 90 degrees, we take the negative value:
cosθ = -1.

Therefore, θ = 180 degrees, which means the wedge C is horizontal in the opposite direction.


From step