Question

Two particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the strings so that they complete their circular path with equal time period is:

• A. $\sqrt{\frac{2}{3}}$
• B. $1$
• C. None of these
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is A $\sqrt{\frac{2}{3}}$

FORMULA USED: $T=2\pi \sqrt{\frac{L\cos \theta }{g}}$

Given: ${\theta }_1={30}^{\circ },{\theta }_2={45}^{\circ }$

As both the pendulums have same time period

$L_1\cos {\theta }_1=L_2\cos {\theta }_2$

$\frac{L_1}{L_2}=\frac{\cos {\theta }_2}{\cos {\theta }_1}=\frac{\cos {45}^{\circ }}{\cos {30}^{\circ }}=\frac{\sqrt{2}}{\sqrt{3}}$