Question

A body of mass $M$ is being pulled by a string of mass $m$ with a force $P$ applied at one end, vertically. The force exerted by the string on the body will be:

• A. $\frac{Pm}{(M+m)}$
• B. $\frac{PM}{(M+m)}$
• C. $Pm(M+m)$
• D. $\frac{P}{(M-m)}$

Answer 1

The correct option is B $\frac{PM}{(M+m)}$

As seen from the free body diagram, we have:

For the string of mass 'm',

$P-mg-F=ma$

For the body of mass M,

$F-Mg=Ma$

Adding, we have:

$p-mg-Mg=Ma+ma$

$⟹a=\frac{P}{M+m}-g$

Force exerted by string on the body $F=M(g+a)$

Substituting the value of $a$ in it, we have:

$F=M(g+\frac{PM}{m+M}-g)$

$⟹F=\frac{PM}{M+m}$