Q. 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) 10$\ r.p.m.$
C) 20$\ r.p.m.$
D) 14$\ r.p.m.$
Explanation
(a) $T = m\omega^{2}r\ \Rightarrow \ \omega \propto \sqrt{T}\ \therefore\frac{\omega_{2}}{\omega_{1}} = \sqrt{\frac{1}{4}} \Rightarrow \omega_{2} = \frac{\omega_{1}}{2} = 5\ rpm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.