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  4. With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is 2 / 3 of the weight?

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Q. With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $2 / 3$ of the weight?

AIIMSAIIMS 2017

Solution:

If man slides down with same acceleration then, its apparent weight decreases.
As the critical condition given is that, rope can bear only $2 / 3$ of his weight. If $a$ is minimum acceleration,
Breaking strength $=m(g-a)$
$=\frac{2}{3} m g$
$\Rightarrow a=g-\frac{2 g}{3}=\frac{g}{3}$