Question

In the following arrangement table and pulley are smooth. Rope is ideal. The monkey of mass m moves upward with respect to the rope with acceleration a,. Find acceleration of block.​

Answer 1

Answer:

b is the ans

Explanation:

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Answer 2

a) m(a + g)/(M + m) is the solution.

Given,

• A rope pulley system in the diagram.

• Relative acceleration of monkey with respect to rope is a.

To find,

Acceleration of block.

Solution,

Let us assume that the acceleration of rope is -a'. Then the actual acceleration of the monkey will be,

a = Acceleration of monkey - (-a')

Acceleration of monkey = a - a'

Forced acting on the monkey,

• The monkey pushes the rope downwards and in return, the rope pulls the monkey upwards.

• Weight acting downwards due to the earth's gravitational field.

Using this we have the equation,

T - mg = m( a - a' ) ---eq(1)

Similarly, for the block of mass M, the only force acting will be Tension in the rope. No frictional force is present as the surface given is smooth.

We have,

     T = Ma' ---eq(2)

     m(a - a' ) +mg = Ma'

     m (a + g ) = a' (M +m)

     m(a + g)/(M + m)$m/s^{2}$ = a'

Therefore, the acceleration of the block of mass M is   m(a + g)/(M + m)$m/s^{2}$