The remaining volume of a glass vessel is constant at all temperature if `(1)/(x)` of its volume is filled with mercury. The coefficient of volume expansion of mercury is 7 times that of glass. The value of x should be

Options

A. 5
B. 7
C. 6
D. 8

Answer

B

Explanation

Let temperature is increased by `DeltaT`.
`V_g-V_(Hg)=V-(V)/(x)` at all temperature
`V[1+gamma_gDeltaT]-(V)/(x)[1+gamma_(Hg)DeltaT]=V-(V)/(x)`
`impliesgamma_g=(gamma_(Hg))/(x)impliesgamma_g=(7gamma_g)/(x)impliesx=7`