8. A weight is attached to the free end of a sonometer wire. It gives resonance at a length 40 cm when it is resonanced with a tuning fork of frequency 512. The weight is then immersed wholly in water, the resonant length is reduced to 30 cm. The relative density in which weight suspended is (A) 16/9 (B) 16/7 (C) 16/5 (D) 16/3

v(frequency) is proportional to W^1/2 /lamda

so for constant frequency , lamda proportional to W^1/2                 (lamda is wavelength)

so, (lamda)₁/(lamda)₂  =  (W₁/W₂₎^1/2 

      L₁/L₂ = (W₁/W₂₎^1/2

W₁ = DVg ,W₂ = DVg -D_wVg  &   L₁ = 40 ,L₂ =30           (D is dencity of material and D_w is dencity of water)

   now ,

            40/30 = (DVg/DVg - D_wVG)^1/2

          D/D_w = 16/7