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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.
(a) \( \gamma_{\ell}=\frac{w_{2}-w_{1}}{\left(w_{0}-w_{2}\right)\left(t_{2}-t_{1}\right)}+\frac{\beta\left(w_{0}-w_{1}\right)}{\left(w_{0}-w_{2}\right)} \)
(b) \( \gamma_{\ell}=\frac{w_{1}+w_{2}}{\left(w_{0}-w_{2}\right)\left(t_{2}-t_{1}\right)}-\frac{\beta\left(w_{0}+w_{1}\right)}{\left(w_{0}-w_{2}\right)} \)
(c) \( \gamma_{\ell}=\frac{w_{2}-w_{1}}{\left(w_{2}-w_{0}\right)\left(t_{2}-t_{1}\right)}+\frac{\beta\left(w_{0}+w_{1}\right)}{\left(w_{0}-w_{2}\right)} \)
(d) \( \gamma_{\ell}=\frac{w_{2}-w_{1}}{\left(w_{2}-w_{0}\right)\left(t_{2}-t_{1}\right)}+\frac{\beta\left(w_{0}-w_{1}\right)}{\left(w_{0}-w_{2}\right)} \)
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