Question

A simple pendulum of length '$l$' has maximum angular displacement '$\theta$'. The maximum kinetic energy of the bob of mass 'm' is :
(g = acceleration due to gravity)

• A. $mgl(1+cos\theta )$
• B. $mgl(1+co{s}^2\theta )$
• C. $mgl(1-cos\theta )$
• D. $mgl(cos\theta -1)$

Answer 1

The correct option is C $mgl(1-cos\theta )$

Kinetic energy of the bob is maximum at the mean position of oscillation i.e. at point A and conservation of energy states that this kinetic energy is converted into the potential energy as the bob reaches at the maximum height i.e. point B.

From figure, we get that $AC=AO-OC$

$\therefore$ $AC=l-l\cos \theta =l(1-cos\theta )$

Potential energy of bob at point B $P.E=mg\left(AC\right)$

$\therefore$ $P.E=mgl(1-\cos \theta )$

Thus maximum kinetic energy of the bob $K.E_{max}=mgl(1-\cos \theta )$