Question

Two light strings, each of length $l$, are fixed at points $A$ and $B$ on a fixed horizontal rod $xy$. A small bob is tied by both strings and in equilibrium, the strings are making angle $45^{\circ }$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be :

• A. $2\pi \sqrt{\frac{2\sqrt{2}l}{g}}$
• B. $2\pi \sqrt{\frac{\sqrt{2l}}{g}}$
• C. $2\pi \sqrt{\frac{l}{g}}$
• D. $2\pi \sqrt{\frac{l}{\sqrt{2}g}}$

Answer 1

Answer: (D)

In given situation if we look at pendulum from
side its effective oscillating length is $\frac{l}{\sqrt{2}}$

Side view of pendulum
Thus angular frequency of oscillations is
$\omega =\sqrt{\frac{g}{l_{eff}}}=\sqrt{\frac{\sqrt{2}g}{l}}$
$\Rightarrow T=2\pi \sqrt{\frac{1}{\sqrt{2}g}}$