Question

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. 3 mg
• D. √3mg

Answer 1

The correct option is A 2 mg

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 + $\frac{m{v}^2}{l}$
= mg + $\frac{m}{l}$[2gl(1 - cos 60)] = mg + mg = 2mg