Question

A simple pendulum is suspended from the fixed point and $m$ is mass of bob. When the bob is at the lowest position, the bob is given a minimum velocity in horizontal direction so that the bob describes vertical circle. When the string is horizontal, the tension in it is:

• A. $6mg$
• B. $\frac{9mg}{2}$
• C. $3mg$
• D. $\frac{3mg}{2}$

Answer 1

Answer: (C)

$3mg$

$Velocityatlowestpoint=\sqrt{5gL}$

Now apply energy conservation between bottom(1) and horizontal(2) point;

$\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2=mg(-L)$

$\frac{1}{2}m{v}_2^2=\frac{1}{2}m{v}_1^2-mgL$

$=\frac{1}{2}m\left(5gL\right)-mgL$

$\Rightarrow V_2^2=3gl$
$V_2=\sqrt{3gl}$

At horizontal position Tension provides centripetal force
$\Rightarrow T=\frac{m{\nu }^2}{R}=3mg$