Question

Find the period of small oscillation of the bob of mass m as shown in the figure. Mass of the rod is m.

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

(1) equilibrium $x_0=\frac{mg}{k}$ rod will bend towards right.

(2) now displace the system x further

(3) note down the energy

$\underset{}{\frac{1}{2}k(X+x_0)}-\underset{}{mgX}+\underset{}{\frac{1}{2}m{v}^2}+\underset{}{\frac{1}{2}l{\omega }^2}=constant$

spring Ball Ball Rod's

Potential Potential kinetic Rotational

Energy Energy Energy Energy

(4) Since total energy is constant $\frac{dE}{dt}=0$

we get $\omega =\sqrt{\frac{3k}{4m}}$

$T=2\pi \sqrt{\frac{4m}{3k}}$