Question

A $2\text{kg}$ ball is swinging in a vertical circle at the end of an inextensible string $2\text{m}$ long. The angular speed of the ball if the string can sustain a maximum tension of $119.6\text{N}$ is (Take $g=9.8{\text{m/s}}^2$)

• A. $5\sqrt{2}\text{rad/s}$
• B. $5\text{rad/s}$
• C. $2\sqrt{2}\text{rad/s}$
• D. $2\text{rad/s}$

Answer 1

The correct option is B $5\text{rad/s}$

Maximum tension will be at the bottom most point :


$T_{max}-mg=\frac{m{v}^2}{R}$
$T_{max}=mg+\frac{m{v}^2}{R}$
We know $v=R\omega$
$\therefore T_{max}=mg+m{\omega }^{2}R$
$\Rightarrow 119.6=2\times 9.8+2\times {\omega }^2\times 2$
$\Rightarrow {\omega }^2=25$
$\Rightarrow \omega =5\text{rad/s}$