First slide

Sonometer

Question

A sonometer wire with a suspended mass of M =1kg is in resonance with a given tuning fork The apparatus is taken to the moon where the acceleration due to gravity is 1/6 that on the earth. To obtain resonance on the moon, the value of M should be

Moderate

A

1 kg
B

$\sqrt{6 kg}$
C

6kg
D

24kg

Solution

$On earth, n_{1} = \frac{1}{2 l} \sqrt{(\frac{Mg}{m})} = \frac{1}{2 l} \sqrt{(\frac{g}{m})} On moon n_{2} = \frac{1}{2 l} \sqrt{(\frac{M (g / 6)}{m})} = \frac{1}{2 l} \sqrt{(\frac{Mg}{6 m})} For resonance, n_{1} = n_{2} ∴ \frac{1}{2 l} \sqrt{(\frac{g}{m})} = \frac{1}{2 l} \sqrt{(\frac{Mg}{6 m})} or M = 6 kg$

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