Question

A $10\text{kg}$ stone is suspended with a rope of breaking strength $30\text{kg-wt}$. The minimum time in which the stone can be raised through a height $10\text{m}$ starting from rest is (taking $g=10\text{N/kg}$)

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

Answer 1

The correct option is B $1.0\text{second}$

The maximum tension $=30\times 10\text{N}=300\text{N}$
$T-mg=ma$
$300-10\times 10=10a$
$\Rightarrow a=20{\text{m/s}}^2$ [Maximum value]
When the mass is raised, $u=0,a=20{\text{m/s}}^2$
$s=10\text{m},t=?$
Using,
$s=ut+\frac{1}{2}a{t}^2$
$10=\frac{1}{2}\times 20\times t^2\Rightarrow t=1\text{second}$
Hence, the correct answer is option (b).