Question

A weightless thread can bear tension up to $30N$. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $2m$ in a vertical plane. If $g=10{ms}^{-2}$, then the maximum angular velocity of the stone will be:

• A. $2rad{s}^{-1}$
• B. $5rad{s}^{-1}$
• C. $8rad{s}^{-1}$
• D. $16rad{s}^{-1}$

Answer 1

The correct option is B $5rad{s}^{-1}$

$T_{max}=\frac{m{v}_{max}^2}{r}+mg$

where $T_{max}$ is maximum tension

$m$ is mass

$x$ is radius

and $g$ is acceleration due to gravity

$T_{max}=m{w}_{max}^{2}r+mg$

where $w=\frac{v}{r}$ is angular velocity

$\frac{T_{max}}{m}=m{w}_{max}^{2}r+g$

$\frac{30}{0.5}=w_{max}^{2}2+10\Rightarrow w_{max}^2=25\Rightarrow w_{max}=5rad/s$