Question

Q 11/75 A uniform rope of mass m is tied to a
block of mass M and a constant force Fis exerted
on the rope in the vertically upward direction as
shown. The force that the rope exerts on the
block, if both move upwards with constant
acceleration is:
m
M​

Answer 1

I hope it helps in some way.

Answer 2

Given:

A regular mass $=M$

Mas of the rope $=m$

To find:

Force exerted by the rope on the mass $M.$

Solution:

We have been given that the mass $M$is tied to the bottom of the rope of mass $m$ and the rope is moving upwards.

We understand that when the rope is moving upwards with (let's assume) acceleration $'a'$ , the block of mass $M$ will also be moving upwards with the same acceleration $'a'$ as both masses will act as a single system.

Hence,

The tension in the string will be nothing but the weight of the system that is

moving with acceleration a upwards.

The force is given by

$F=ma$

$F=(M+m)a$

$a=\frac{F}{(M+m)}$

Hence, the system moves upwards with acceleration $\frac{F}{(M+m)}$.

Now,

For the system to move upwards, the external force exerted on pulling of the rope should be greater than the weight of the block.  

$F_{ext}$ > $Ma$

and, we have thee value of a as $\frac{F}{(M+m)}$

Therefore, the force exerted on the block will be

$F_{ext} =M\frac{F}{M+m}$

Final answer:

Hence, the rope exerts a force of $M\frac{F}{M+m}$ on the block.