Question

A solid floats in a liquid at 20${}^0$C with 75% of it immersed in a liquid. When the liquid is heated to 100${}^0$C the same body floats with 80% of it immersed in the liquid. The coefficient of real expansion of the liquid is

• A. $8\times {10}^{-4}{/}^{0}C$
• B. $8.33\times {10}^{-4}{/}^{0}C$
• C. $8.33\times {10}^{-5}{/}^{0}C$
• D. $8\times {10}^{-5}{/}^{0}C$

Answer 1

Answer: (B)

$8.33\times {10}^{-4}{/}^{0}C$

For the body to float with 75% inside liquid, the buoyant force at that temperature must be equal to its weight,

$⟹Mg=0.75V{\rho }_{{20}^{\circ }}g$

Similarly for body to float with 80% inside liquid, the buoyant force at that temperature must be equal to its weight,

$⟹Mg=0.80V{\rho }_{{100}^{\circ }}g$

$\frac{{\rho }_{{100}^{\circ }}}{{\rho }_{{20}^{\circ }}}=\frac{0.75}{0.80}=\frac{1}{1+\gamma \Delta T}$

$⟹\gamma =8.33\times {10}^{-4}{/}^{\circ }C$