Question

A ball of mass 0.1 kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 r.p.m. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is

• A. 5 r.p.m.
• B. 10r.p.m.
• C. 20r.p.m
• D. 14r.p.m.

Answer 1

Answer: (A)

5 r.p.m.

Answer 2

Tension in the string $T = m\omega^{2}r = m4\pi^{2}n^{2}r$

$T \propto n^{2}$ or $n \propto \sqrt{T}$ [As m and r are constant]

∴ $\frac{n_{2}}{n_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{T/4}{T}}$ ⇒ $n_{2} = \frac{n_{1}}{2} = \frac{10}{2} = 5rpm$