Q. A stone is tied to one end of a string and rotated in a horizontal circle with a uniform angular velocity. Let $T$ be the tension in the string. If the length of the string is halved and its angular velocity is doubled, tension in the string will be
A) $T/4$
B) $T/2$
C) 2$T$
D) 4$T$
Explanation
(c) Tension in the string
$T = mv^{2}/r = (r\omega)^{2} = mr\omega^{2}$
If $r_{1} = r/2$ and $\omega_{1} = 2\omega,$ then
$T_{1} = m(r/2)(2\omega)^{2} = 2mr\omega^{2} = 2T$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.