Question

In a cylindrical glass container a solid silica silica is placed vertically at its bottom and remaining space is filled with mercury upto the top level of the silica cylinder as shown in the figure-$1.26$. Assume that the volume of the silica remains unchanged due to variation in temperature. The coefficient of cubical expansion of mercury is $\gamma$ and coefficient of linear expansion of glass is $\alpha$. If the top surface of silica and mercury level remain at the same level with the variation in temperature then the ratio of volume of silica to the volume of mercury is equal to :

• A. $\frac{\gamma}{2 \alpha}$
• B. $\frac{\gamma}{3 \alpha}$
• C. $\frac{\gamma}{2 \alpha}-1$
• D. $\frac{\gamma}{3 \alpha}-1$

Answer 1

Answer: (C)

If $A_{1}$ is cross sectional area of silica cylinder, $\left(A_{1}+A_{2}\right)$ is cross sectional area of glass cylinder, and $h$ is the height of silica cylinder, then :
$h\left(A_{1}+A_{2}\right)(2 \alpha) \Delta \theta=h\left(A_{2}\right) y \Delta \theta$
$\Rightarrow \frac{h A_{1}}{h A_{2}}=\left(\frac{\lambda}{2 \alpha}-1\right)$
$\Rightarrow \frac{\text { volume of silica }}{\text { volume of mercury }}=\left(\frac{\lambda}{2 \alpha}-1\right)$