Question

A mass of $2\text{kg}$ is whirled in a horizontal circle by means of a string at an initial speed of $5\text{rpm}$. Keeping the radius constant the tension in the string is doubled. The new speed is nearly.

• A. $\frac{5}{\sqrt{2}}\text{rpm}$
• B. 10 rpm
• C. $10\sqrt{2}\text{rpm}$
• D. $5\sqrt{2}\text{rpm}$

Answer 1

The correct option is D $5\sqrt{2}\text{rpm}$

Tension in the string $T=m{\omega }^{2}r=4{\pi }^2{n}^2\text{mr}$
$\therefore T\propto n^2$
$\Rightarrow \frac{n_2}{n_1}=\sqrt{\frac{T_2}{T_1}}$
$\Rightarrow n_2=5\sqrt{\frac{2T}{T}}=5\sqrt{2}\text{rpm}$.