Question

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

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

Answer 1

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

$T_1=2\pi \sqrt{\frac{left}{g}}$ $T_2=2\pi \sqrt{\frac{left}{g}}$

$T_1=2\pi \sqrt{\frac{lcos{30}^{\circ }}{g}}$ $T_2=2\pi \sqrt{\frac{lcos{45}^{\circ }}{g}}$

SINCE from above question

$T_1^2=T_2^2$

$\frac{L_1}{L_2}=\frac{2}{\sqrt{2}}\times \frac{1}{\sqrt{3}}$

$\frac{L_1}{L_2}=\sqrt{\frac{2}{3}}$

Hence (B) is the correct answer