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A stone is hung in air from a wire which...

A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are L cm apart when the wire is in unison with a tuning fork of frequency N . When the stone is completely immersed in water, the length between the bridges is l cm for re-establishing unison, the specific gravity of the material of the stone is

A

`(L^(2))/(L^(2)+l^(2))`

B

`(L^(2)-l^(2))/(L^(2))`

C

`(L^(2))/(L^(2)-l^(2))`

D

`(L^(2)+l^(2))/(L^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`f=(1)/(2l)sqrt((T)/(mu))`
When the stone is completely immersed in water, length changes, but frequency remains constant
`lpropsqrt(T)implies(L)/(l)=sqrt((T_("air"))/(T_("water")))=sqrt((V_(rhog))/(V(rho-1)g))`
`implies (L)/(l)=sqrt((rho)/(rho-1))impliesrho=(L^(2))/(L^(2)-l^(2))`.
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