Q. A mass of $2\ kg$ is whirled in a horizontal circle by means of a string at an initial speed of 5 $revolutions\ per\ minute.\ $Keeping the radius constant the tension in the string is doubled. The new speed is nearly
A) $14\ rpm$
B) $10\ rpm$
C) $2.25\ rpm$
D) $7\ rpm$
Explanation
(d) Tension in the string $T = m\omega^{2}r = 4\pi^{2}n^{2}mr$
$\therefore T \propto n^{2} \Rightarrow \frac{n_{2}}{n_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow n_{2} = 5\sqrt{\frac{2T}{T}} = 7\ rpm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.