An iron load of 2Kg is suspended in the air from the free end of a sonometer wire of length 1m.A tuning frok of frequency 256 Hz, is in resonace with `1/sqrt7` times the length of the sonometer wire. If the looad is immersed in water, the length of the wire in metre that will be in resonance with the same tuning fork is (specific gravity of iron=8)

Options

A. `sqrt8`
B. `sqrt6`
C. `1/sqrt6`
D. `1/sqrt8`

Answer

D

Explanation

In air ,`n=l/(2l)sqrt(T/m)`
`implieslalphasqrtT`
`l_(air)/(l_(water))=sqrt(T_(air)/(T_(water))`
Specific gravity =8
`8=T_(air)/(T_(air)-T_(water))`
`8(T_(air)-T_(water))=T_(air)`
`T_(water)=7/8T_(air)`
`implies l_(air)/l_(water)=sqrt(8/7)` but ` l_(air)=1/sqrt7l`
` l_(water)=1/sqrt8l`