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

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

Option: 1

\sqrt{\frac{3}{2}}


Option: 2

\sqrt{\frac{2}{3}}


Option: 3

1


Option: 4

\sqrt{\frac{4}{5}}


Answers (1)

best_answer

Time period is equal , T_{1}=T_{2}
                           \begin{aligned} & 2 \pi \sqrt{\frac{l_1 \cos \theta_1}{g}}=2 \pi \sqrt{\frac{l_2 \cos \theta_2}{g}} \\ & \frac{l_1 \cos \theta_1}{g}=\frac{l_2 \cos \theta_2}{g} \\ & \frac{l_1}{l_2}=\frac{\cos \theta_2}{\cos \theta_1}-------(1) \end{aligned}
Now , \Theta_{1} = 30^{0} , \Theta _{2}=45^{\circ} , put\ in \left ( 1 \right )-
\frac{l_1}{l_2}=\frac{\cos 45^{\circ}}{\cos 30^{\circ}}=\frac{1 / \sqrt{2}}{\sqrt{3} / 2}=\frac{1}{\sqrt{2}} \times \frac{2}{\sqrt{3}} \times\left(\frac{\sqrt{2}}{\sqrt{2}}\right)
\frac{l_1}{l_2}=\frac{2 \sqrt{2}}{2 \sqrt{3}}=\sqrt{\frac{2}{3}}

Posted by

Ritika Jonwal

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