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. $2 m g$
• B. 1 $m g$
• C. $3 m g$
• D. $\sqrt { 3 } m g$

Answer 1

Answer: (A)

$2 m g$

Answer 2

When body is released from the position p (inclined at angle θ from vertical) then velocity at mean position

$v = \sqrt { 2 g l ( 1 - \cos \theta ) }$

∴ Tension at the lowest point

= $m g + \frac { m v ^ { 2 } } { l }$

$= m g + \frac { m } { l } [ 2 g l ( 1 - \cos 60 ) ]$ $= m g + m g = 2 m g$