Question

A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force on the block of mass $m$.

• A. $\frac{mF}{M}$
• B. $\frac{(M+m)F}{m}$
• C. $\frac{mF}{(m+M)}$
• D. $\frac{MF}{(m+M)}$

Answer 1

The correct option is C $\frac{mF}{(m+M)}$

Given two blocks of masses $M$ and $m$, And

a force $F$ acting on the block of mass $M$ pulling it outside

The two masses system can be considered as a whole, With $F$

being the only $external$ force acting on them.

Here the spring force has been ignored as while considering the two system as a whole, it will be accounted as an $internal$ force for the system

Therefore, The acceleration of the system will be

$a$ = $\frac{Totalexternalforce}{Totalmass}$

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

Now both the masses are moving with this $same$ acceleration towards the direction of force

Acceleration of mass $m$ = $a$ (as the system is moving as a whole)

Force on the mass m= mass times acceleration

Force = $ma$

= $\frac{mF}{m+M}$