Question

A $10$$kg$ stone is suspended with a rope of breaking strength $30$$kg.wt.$ The minimum time in which the stone can be raised through a height $10$$m$ starting from rest is:
(Taking $g=10Nk{g}^{-1}$)

• A. $0.5$$s$
• B. $1.0$$s$
• C. $\sqrt{\frac{2}{3}}$$s$
• D. $2.0$$s$

Answer 1

Answer: (B)

$1.0$$s$

Maximum acceleration allowed after which the rope breaks = $\frac{F_{max}}{m}$

$=\frac{30\times 10}{10}=30m/s^2$

Acceleration due to gravity is already present due to suspension of stone.

Thus acceleration upto which the stone can be lifted with = $a_{max}-g=a=20m/s^2$

$s=\frac{1}{2}a{t}^2$

$⟹t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 10}{20}}=1s$