A block of mass m is connected to another block of mass M by a spring (massless) of spring constant

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4-1.Newton's Laws of Motion

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A block of mass $m$ is connected to another block of mass $M$ by a spring (massless) of spring constant $k$. The block 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 of the block of mass $m.$

A

$\frac{{MF}}{{\left( {m + M} \right)}}$

B

$\frac{{nF}}{M}$

C

$\;\frac{{\left( {m + M} \right)F}}{m}$

D

$\;\frac{{mF}}{{\left( {m + M} \right)}}$

(AIEEE-2007)

Solution

Drawing free body – diagrams for $m \& M$,

we get $T=m a$ and $F-T=M a$

Where $T$ is force due to spring

$\Rightarrow F-m a=M a$ or $, F=M a+m a$

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

Now, force acting on the block of mass

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

Standard 11

Physics

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