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(C) The frequency of a sonometer wire is given by $n = \frac{1}{2 \ell} \sqrt{\frac{T}{\mu}}$,where $T = Mg$ is the tension in the wire and $\mu$ is t

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$6$

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(C) The frequency of a sonometer wire is given by $n = \frac{1}{2 \ell} \sqrt{\frac{T}{\mu}}$,where $T = Mg$ is the tension in the wire and $\mu$ is the linear mass density.Thus,$n = \frac{1}{2 \ell} \sqrt{\frac{Mg}{\mu}}$.For the wire to be in resonance with the same tuning fork,the frequency $n$ must remain constant.Since $\ell$ and $\mu$ are constant,we have $n \propto \sqrt{Mg}$.Therefore,$\sqrt{M_1 g_1} = \sqrt{M_2 g_2}$.Given $M_1 = 1 \, kg$,$g_1 = g$,and $g_2 = g/6$.Substituting these values: $\sqrt{1 	imes g} = \sqrt{M_2 	imes \frac{g}{6}}$.Squaring both sides: $g = M_2 	imes \frac{g}{6}$.Solving for $M_2$,we get $M_2 = 6 \, kg$.

$A$ sonometer wire,with a suspended mass of $M = 1 \, kg$,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 earth. To obtain resonance on the moon,the value of $M$ should be ......... $kg$.

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