The loss of weight of a solid when immersed in a liquid at `0^(@)C` is `W_(0)` and at `t^(@)C` is `'W'`. If cubical coefficient of expansion of the solid and the liquid are `gamma_(s)` and `gamma_(1)` then `W =`

Options

A. `W_0[1+(gamma_S-gamma_L)t]`
B. `W_0[1-(gamma_S-gamma_L)t]`
C. `W_0[(gamma_S-gamma_L)t]`
D. `W_0 t//(gamma_S-gamme_L)`

Answer

A

Explanation

`U_0=V_0sigma_L^0g=W_0` and `U_t=V_tsigma_L^(t)g=W`
`(W)/(W_0)=(V_t)/(V_0)xx(sigma_L^t)/(sigma_L^0)=((1+gamma_BDeltatheta))/((1+gamma_LDeltatheta))`
`=(1+gamma_SDeltatheta)(1+gamma_LDeltatheta)^-1=1+gamma_SDeltatheta-gamma_LDeltatheta`
`=W=W_0[1+(gamma_S-gamma_L)Deltatheta)]`
`=W_0[1+(gamma_S-gamma_L)t]`