Question

A $2kg$ stone is tied to a string of $2m$ length & is whirled in a horizantal circle. If the breaking tension of the string is $400N$, the maximum velocity of the stone in $m{s}^{-1}$ is :

• A. $40$
• B. $20$
• C. $10$
• D. $50$

Answer 1

Answer: (B)

$20$

Mass of stone(m) = $2Kg$,

radius(r) = length of rope $=2m$,

Maximum tension $\left(T_{max}\right)$ = $400N$

The maximum tension acts as the centripetal force for the circular motion of the stone.

Let $v_{max}$ be the maximum velocity.

Hence, $F=T_{max}=\frac{m{v}_{max}^2}{r}$

$\Rightarrow v_{max}^2=\frac{T_{max}\times r}{m}$

$\Rightarrow v_{max}=\sqrt{\frac{T_{max}\times r}{m}}$

$\Rightarrow v_{max}=\sqrt{\frac{400\times 2}{2}}$

$\Rightarrow v_{max}=20m{s}^{-1}$