Question

A platinum sphere floats in mercury. Find the percentage change in the fraction of volume of sphere immersed in mercury when the temperature is raised by ${80}^{\circ }C$ (Volume expansivity of mercury is $182\times {10}^{-6}{/}^{\circ }C$ and linear expansivity of platinum is $9\times {10}^{-6}{/}^{\circ }C$)

• A. $1.24$
• B. $1.38$
• C. $2.48$
• D. $2.76$

Answer 1

The correct option is A

$1.24$

$\frac{V^{\prime }}{V}$ = $\frac{\rho }{\sigma }$ = Fraction of volume of sphere submerged = $\eta$(say)

To find $\%$ change in $\eta$, i.e., $(\frac{{\eta }^{\prime }}{\eta }-\eta )\times 100$

Or $(\frac{{\eta }^{\prime }}{\eta }-\eta )\times 100$ = $[\frac{(\frac{\rho }{\sigma }{)}^{\prime }}{\left(\frac{\rho }{\sigma }\right)}-1]\times 100$

= $\left[\frac{(1+{\gamma }_m\Delta T)}{(1+{\gamma }_p\Delta T)}\right]\times 100\simeq ({\gamma }_m-{\gamma }_p)\Delta T\times 100$

= $(182-27)\times {10}^{-6}\times 100$ = $1.24\%$