Question

The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $u=\sqrt{10gl}$, where $l$ is the length of the pendulum. Find the velocity of the bob when the string is horizontal.

• A. $\sqrt{2gl}$
• B. $\sqrt{4gl}$
• C. $\sqrt{6gl}$
• D. $\sqrt{8gl}$

Answer 1

The correct option is D $\sqrt{8gl}$


Let the velocity at B be $v_b$ .
The velocity at A is $u=\sqrt{10gl}$ (given)
Applying energy conservation at $A$ & $B$, taking $A$ as reference.
$(KE{)}_A=(KE{)}_B+(PE{)}_B$
$\frac{1}{2}m{u}^2=\frac{1}{2}m{v}_B^2+mgl$
$\Rightarrow \frac{1}{2}m\left(10gl\right)=\frac{1}{2}m{v}_B^2+mgl$
$\Rightarrow 8mgl=m{v}_B^2$
$\Rightarrow v_B^2=8gl$ ---------(1)
or $v_B=\sqrt{8gl}$