Question

Figure shows a platform on which a man of mass $M$ is standing and holding a string passing over a system of ideal pulleys. Another mass $m$ is hanging as shown in figure. Consider the entire system to be in equilibrium. Take $M=5m$, find the force exerted by the platform on man.

• A. $\text{mg}$
• B. $2\text{mg}$
• C. $3\text{mg}$
• D. $4\text{mg}$

Answer 1

The correct option is A $\text{mg}$


If tension in string which the man is holding is $T$, the tension in the string to which the mass $m$ is connected is $\frac{T}{4}$ which must balance $mg$. Thus we have
$T=4\text{mg}$ = force exerted by man on string.
If the force, which platform is exerting on man is $N$, for equilibrium of man we must have
$\text{N + T = Mg}$ $(\because M=5m)$
or $\text{N = Mg - 4 mg = 5mg - 4mg = mg}$