A sinker of weight `w_0` has an apparent weight `w_1` when weighed in a liquid at a temperature `t_1 and w_2` when weight in the same liquid at temperature `t_2`. The coefficient of cubical expansion of the material of sinker is `beta`. What is the coefficient of volume expansion of the liquid.

Answer

A, B

Explanation

`W_0-W_1=Vxxd_lxxg…..(i)`
`W_0-W_2=V'xxd'_lxxg…..(ii)`
Also, `V'=V(1+betaDeltaT)…..(iii)`
and `d_l=d'_l(1+gamma_lDeltaT)….(iv)`
From (ii),(iii) and (iv)
`W_0-W_2=(V(1+betaDeltaT)xxd_l)/(1+gamma_lDeltaT)xxg….(v)`
Dividing (ii) and (v), we get
`(W_0-W_1)/(W_0-W_2)=(Vd_lg(1+gammaDeltaT))/(V(1+betaDeltaT)xxd_lg)`
`(W_0-W_1)/(W_0-W_2)=(1+gamma_lDeltaT)/(1+beta_lDeltaT) rArr (W_0-W_1)/(W_0-W_2)=(1+gamma_l(t_2-t_1))/(1+beta(t_2-t_1))`
`(W_0-W_1)[1+beta(t_2-t_1)]=(W_0-W_2)[1+gamma_l(t_2-t_1)]`
`rArrgamma_l=(W_2-W_1)/((W_0-W_2)(t_2-t_1))+(beta(W_2-W_1))/(W_0-W_2)`