Question

A man slides down a light rope whose breaking strength $\eta$ times the weight $(\eta <1)$. The maximum acceleration of the man so that the rope just breaks is:-

• A. $g(1-\eta )$
• B. $g(1+\eta )$
• C. $g\eta$
• D. $\frac{g}{\eta }$

Answer 1

The correct option is A $g(1-\eta )$

Breaking strength $=$ $-$ maximum tension

Given that

$T=\eta \times$ weight of man $=\eta \times mg$

From Newton's law of motion

$mg-T=ma$

$mg-\eta mg=ma$

$mg(1-\eta )=ma$

$a=(1-\eta )g$

Given that, $\eta <1$. So, acceleration is downwards because $(1-\eta )>0$

So, $a=(1-\eta )g$ option (A) correct.