A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are `gamma_1` and `gamma_2` respectively. If the temperatures of both mercury and the metal are increased by an amount `DeltaT`, the fraction of the volume of the metal submerged in mercury changes by the factor............

Options

A. `(1)/((gamma_(2) - gamma_(1))Deltat)`
B. `(1)/((gamma_(1) - gamma_(2))Deltat)`
C. `(gamma_(1) - gamma_(2))`
D. `(gamma_(2) - gamma_(1)) Deltat`

Answer

D

Explanation

`f_(1) = (d_(metel))/(d_(mercury)), f_(2) = (d_(metal))/((1 + gamma_(1)Deltat)) xx ((1 + Delta_(2)t))/(d_(mercury))`
`f_(2)/(f_(1))=((1+gamma_(2)Delta_(t)))/((1+gamma_(1)Deltat)),(f_(2) - f_(1))/(f_(1))=(gamma_(2)-gamma_(1))Deltat`