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

1 Answer
Ashley H
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=ma...........................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=Ma'# (where, #a'# is the acceleration of the larger block)

Putting #R=Ma'# in #1# we get,

#F-Ma'=ma#

or, #a'=(F-ma)/M#

and, #R=F-ma# (from #1#)

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