8. A weight is attached to the free end of a sonometer wire. It gives resonance at a length 40 cm when it isresonanced with a tuning fork of frequency 512. The weight is then immersed wholly in water, the resonantlength 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