Q. A body of mass $m$ hangs at one end of a string of length $l$, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of $60{^\circ}$ with the vertical. The tension in the string at mean position is
A) $2\ mg$
B) $mg$
C) $3mg$
D) $\sqrt{3}mg$
Explanation
(a) When body is released from the position $p$ (inclined at angle $\theta$ from vertical) then velocity at mean position
$v = \sqrt{2gl(1 - \cos{\theta)}}$
$\therefore$ Tension at the lowest point $= mg + \frac{mv^{2}}{l}$
$= mg + \frac{m}{l}\left\lbrack 2gl\left( 1 - \cos 60 \right) \right\rbrack = mg + mg = 2mg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.