Question

A 10kg stone is suspended with a rope of breaking strength 30kg-wt. The minimum time in which the stone can be raised through a height of 10m is

Answer 1

Mass of stone = $10\ kg$

Breaking strength of rope = $30\ kg\ wt=30g\ =300\ N$

Let the maximum allowed acceleration be $a$

So

Breaking strength $=300=mg+ ma=100+10a$

$10a=200\\So,\\a=20\ m\ s^{-2}$

$h=10\ m\\let\ \ t\ \ be\ time \ taken\\$

$u=0\\using\ equation\ of \ motion\\h=ut+\frac{at^2}{2}=10$

So,

$t=\sqrt\frac{20}{a}=\sqrt\frac{20}{20}= 1\ sec ond$