Question

A pendulum bob is raised to a height, $h$, and released from rest. At what height will it attain half of its maximum speed?

• A. $\frac{3h}{4}$
• B. $\frac{h}{2}$
• C. $\frac{h}{4}$
• D. $0.707h$

Answer 1

Answer: (A)

$\frac{3h}{4}$

By energy conservation, $\frac{1}{2}m{v}_{max}^2=mgh$
Let at height $h^{\prime }$, it attain velocity $v^{\prime }=\frac{v_{max}}{2}=\sqrt{gh/2}$
Now, $mgh=\frac{1}{2}m{v}^{\prime 2}+mg{h}^{\prime }$

or $mgh=\frac{mgh}{4}+mg{h}^{\prime }$

or $mg{h}^{\prime }=\frac{3}{4}mgh$

$\therefore h^{\prime }=\frac{3h}{4}$