# Two bodies. X and Y of mass m and M respectively exert forces on each other and no other forces act on them. The force on X is F and the acceleration is a. Which of the following pairs is correct?

## Magnitude of force on Y Magnitude of acceleration of Y A. m/M x F a B. F ma/M

Aug 11, 2018

Here,the force on the smaller block will be the reactional force exerted by the larger block on it and vice versa.

If,that force is $R$ we can say,this force will act against the direction of applied force $F$ on the smaller block.

Given,its acceleration is $a$

So,we can say, $F - R = m a \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots 1$

For,the larger block,the reaction force by the smaller block is acting to cause its movements,but as there is no frictional force,it will also move,so we can write for it as,

$R = M a '$ (where, $a '$ is the acceleration of the larger block)

Putting $R = M a '$ in $1$ we get,

$F - M a ' = m a$

or, $a ' = \frac{F - m a}{M}$

and, $R = F - m a$ (from $1$)