Question

A mass of $2$ kg is whirled in a horizontal circle by means of a string at an initial speed of $5$ r.p.m. Keeping the radius constant the tension in the string is doubled. The new speed is nearly?

• A. $7$ r.p.m.
• B. $14$ r.p.m.
• C. $10$ r.p.m.
• D. $20$ r.p.m.

Answer 1

The correct option is A $7$ r.p.m.

$mass=2kg$

$Initialspeed=\omega =5rpm$

$=\frac{5\times 2\pi }{60}\frac{rad}{sec}=\frac{\pi }{6}\frac{rad}{sec}$

$Tension=Centripetalforce=mr\omega ²$

$T=2\times r\times \left(\frac{\pi }{6}\right)²$

$T=mr\omega ²=\frac{2\times r\times \pi ²}{36}$ If tension is doubled, centripetal force also will be doubled.

$2T=mr\omega ₁²$

$=2\times [\frac{2\times r\times \pi ²}{36}$ where $\omega ₁²$ is the new angular speed Dividing by we get

$\omega ₁²=2\omega ²\omega ₁$

$=\sqrt{2\omega }$

$=\sqrt{2\times 5}\approx 7rpm$

New angular speed will be $\sqrt{2}$times initial angular speed.