First slide

Circular motion in horizontal plane

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:

Moderate

A

$\sqrt{\frac{3}{2}}$
B

$\sqrt{\frac{2}{3}}$
C

1
D

None of these

Solution

Since $T = 2 π \sqrt{\frac{L \cos θ}{g}}$
$∴ T_{1} = T_{2}$
$\Rightarrow L_{1} \cos θ = L_{2} \cos θ_{2}$
$∴ \frac{L_{1}}{L_{2}} = \frac{\cos θ_{2}}{\cos θ_{1}} = \frac{\cos 45^{0}}{\cos 30^{0}}$
$\frac{L_{1}}{L_{2}} = \frac{\sqrt{2}}{\sqrt{3}}$

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