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

Question

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is 2 / 3 of the weight? (A) 2 /3 g (B) g (C) 1 /3 g (D) zero

Tardigrade Admin · Accepted Answer

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}

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

2 /3 g

g

1 /3 g

zero

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) =32​mg ⇒a=g−32g​=3g​

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

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 $= m (g - a)$
$= \frac{2}{3} m g$
$\Rightarrow a = g - \frac{2 g}{3} = \frac{g}{3}$