Question

A rod with a circular cross-section oscillates about a horizontal axis passing through one of its end and it behaves like a seconds pendulum. Its length will be

• A. $1.5m$
• B. $1m$
• C. $3m$
• D. $2m$

Answer 1

Answer: (A)

$1.5m$

For a seconds pendulum we have the time period as 2 seconds.
Thus using the expression for time period of compound pendulum we get
$T=2\pi \sqrt{\frac{I}{mgR}}$
or
$2=2\pi \sqrt{\frac{\frac{m{l}^2}{3}}{mg\frac{l}{2}}}$
or
$\sqrt{\frac{3g}{2l}}=\pi$
or
$\frac{{\pi }^2}{g}l=\frac{3}{2}$
or
$l=\frac{3}{2}=1.5m$