A bob is whirled in a horizontal circle by means of a string at an initial speed of 20 rpm. If the t

Question

A bob is whirled in a horizontal circle by means of a string at an initial speed of 20 rpm. If the tension in the string is increased 9 times while keeping the radius constant, the new speed is

Professor PC Thomas Classes · Answer

Tension provides the necessary centripetal force: $T = mr\omega^2$. If tension is increased by a factor of 9 ($T' = 9T$), we get $9T = mr(\omega')^2$. Dividing both equations gives $9 = (\omega' / \omega)^2 \implies \omega' = 3\omega$. Hence, $\omega' = 3 	imes 20 = 60 \mathrm{~rpm}$.