Question

As shown in figure, a man of mass $M$ is standing on a platform and holding an inextensible massless string which passes over a system of ideal pulleys. Another body of mass $m$ is hanging as shown in figure. Find the force exerted by the platform on man if $M=50\text{kg},m=10\text{kg}$, Take $g=10{\text{m/s}}^2$.

• A. $10\text{N}$
• B. $100\text{N}$
• C. $25\text{N}$
• D. $50\text{N}$

Answer 1

The correct option is B $100\text{N}$

If the tension in the string which the man is holding is $T$, the distribution of tension in all strings, considering the pulleys to be massless, is shown in FBD.


Applying equilibrium condition for mass $m$, since system is at rest:
$\frac{T}{4}=mg$
$\therefore T=4mg...\left(i\right)$
From FBD of man, force exerted by platform on man is $N$, hence applying equilibrium condition:


$N+T=Mg...\left(ii\right)$
From Eq. $\left(i\right)$ and $\left(ii\right)$,
$N=Mg-4mg$
$\Rightarrow N=(50\times 10-4\times 10\times 10)$
$\therefore N=100\text{N}$