The mass of the body

attached to the movable pulley is 12 times the mass of the body fixed to the ground. At some instant the
body fixed to the ground is released. What will be the height that it can ascend? The heavier mass is initially h meter above the ground.

one has to know the mechanical advantage of the pulley system. if configured correctly, it could go to 12 h

The answer is 2h.

again,one has to know the MA

Tension T in rope,

on big mass
M g - T = M a

while the big mass is falling, the little mass goes up a distance h

when the big mass hits ground, the little mass is moving with the speed that the big mass hits with, then coasts up until the kinetic energy of that speed is spent. That is another distance h

Well, there is a picture to this question which shows that the tension on the bigger mass is 2T and the tension on the smaller mass is T.

To solve this problem, we can use the principles of mechanical advantage and conservation of energy.

First, let's assign variables to the masses and heights involved:
Let M1 be the mass attached to the movable pulley (12 times the mass of the body fixed to the ground).
Let M2 be the mass attached to the fixed pulley (initially released).
Let h1 be the height of the movable pulley above the ground.
Let h2 be the height of the fixed pulley above the ground.

Given:
M1 = 12M2 (mass of the body attached to the movable pulley is 12 times the mass of the body fixed to the ground)
h1 = h (heavier mass is initially h meters above the ground)

Since the system is in equilibrium when the body fixed to the ground is released, the tension in the rope supporting the movable pulley must be equal to the tension in the rope supporting the fixed pulley.

Now, let's analyze the system step by step:

Step 1: Calculate the force exerted by the heavier mass (M1) hanging on the movable pulley:
The force exerted by M1 is given by:
F1 = M1 * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Step 2: Calculate the tension in the rope supporting the movable pulley:
The tension in the rope supporting the movable pulley is equal to the force exerted by M1, which is F1.

Step 3: Calculate the tension in the rope supporting the fixed pulley:
Since the tension in the rope is the same throughout the system, the tension in the rope supporting the fixed pulley is also equal to F1.

Step 4: Calculate the force exerted by the mass attached to the fixed pulley (M2):
The force exerted by M2 is given by:
F2 = M2 * g

Step 5: Calculate the net force acting on M2:
The net force acting on M2 is given by:
Net force = F2 - Tension (in the direction of motion)
Since M2 is initially at rest, the tension in the rope supporting the fixed pulley is equal to the force exerted by M2 (F2).

Step 6: Calculate the work done on M2 as it ascends:
The work done on M2 is given by:
Work = Force * Distance
In this case, the distance is the height h2 that M2 ascends.

Step 7: Apply the law of conservation of energy:
The work done on M2 is equal to the potential energy gained by M2 as it ascends:
Work = m2 * g * h2

Since Steps 6 and 7 involve the same work done, we can equate them:
m2 * g * h2 = Force * Distance

Now, substituting the values we derived from Steps 1-5, we have:
M2 * g * h2 = F2 * h2 = F1 * h2

Substituting F1 = M1 * g and M1 = 12M2, we have:
12M2 * g * h2 = M2 * g * h2

Simplifying and canceling like terms, we get:
12h2 = 1h2

Therefore, h2 = 0.

This means that the body fixed to the ground will not ascend when it is released. It will remain at its initial height.