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Q.

A stretched wire of 70 cm length fixed at one end has a solid mass M, hanging from its other end to produce tension in it. The wire produces a certain frequency. When the same mass 'M' hange in water, it is found that the length of the wire has to be changed by 5 cm. in order to produce the same frequency. Then the density of the material of mass 'M' is

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a

1 gm / cc

b

5 gm / cc

c

169/27 gm / cc

d

196/27 gm / cc

answer is D.

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Detailed Solution

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$n = \frac{1}{2 l_{1}} \sqrt{\frac{Mg}{μ}}$ in air
$n = \frac{1}{2 l_{2}} \sqrt{\frac{Mg (1 - \frac{ρ_{ω}}{ρ_{B}})}{μ}}$ in water
$l_{2} < l_{1} \Rightarrow \frac{l_{2}}{l_{1}} = \sqrt{1 - \frac{ρ_{w}}{ρ_{B}}} \frac{65}{70} = \sqrt{1 - \frac{ρ_{w}}{ρ_{B}}} \Rightarrow \frac{ρ_{w}}{ρ_{B}} = 1 - {(\frac{13}{14})}^{2} \Rightarrow ρ_{B} = \frac{196}{27} gm / cc$

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