In HC Verma vol.1 pg 81(newton laws of motion ) Ques.32 if there is one movable pulley and a block of Mass 2M is hanging and one pulley is fixed on the top edge of inclined plane and one edge of string is fixed on ceilling and other end is passing from movable pulley then going on fixed pulley and get attched to a block of massM on pulley. if acceleration of mass 2M is a then Mass of M will be 2a? is it because of tension on mass 2M is 2T and on mass M is T?

Question

Answer

Answer

Explanation of the problem:

The given problem involves a movable pulley and a block of mass 2M hanging from it. The other end of the string is attached to a fixed pulley which is placed on the top edge of an inclined plane. The string from the fixed pulley is connected to a block of mass M. It is required to find out the mass of M if the acceleration of the block of mass 2M is a.

Solution:

The solution to this problem can be obtained by applying the laws of motion. The following steps explain the solution to the problem:

1. Consider the forces acting on the block of mass 2M:

- The weight of the block, which acts downwards and has a magnitude of 2Mg, where g is the acceleration due to gravity.
- The tension in the string, which acts upwards and has a magnitude of T.

2. Since the block of mass 2M is accelerating, there must be a net force acting on it. Using Newton's second law, we can write:

2Mg - T = 2Ma

3. Consider the forces acting on the block of mass M:

- The weight of the block, which acts downwards and has a magnitude of Mg.
- The tension in the string, which acts upwards and has a magnitude of T.

4. Since the block of mass M is connected to the movable pulley, it will have the same acceleration as the block of mass 2M. Using Newton's second law, we can write:

T - Mg = Ma

5. Solving the above two equations simultaneously, we get:

T = 2Ma + 2Mg

Substituting this value of T in the equation for the block of mass M, we get:

2Ma + 2Mg - Mg = Ma

Simplifying this equation, we get:

M = 2a

Explanation for the mass of M being 2a:

The mass of M is equal to 2a because the tension in the string on the side of the block of mass 2M is twice the tension on the side of the block of mass M. This is because the string passes through a movable pulley, which changes the direction of the tension force. As a result, the tension in the string is doubled on the side of the block of mass 2M. Therefore, the acceleration of the block of mass M is half that of the block of mass 2M. Hence, the mass of M is equal to 2a.

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