Question

A body is floating in water at 4${}^0$C such that 0.98 of its total volume is immersed in water. If the coefficient of real expansion of water is $3.3\times {10}^{-4/0}C$. The temperature at which the body gets immersed completely is

• A. ${32.8}^{0}C$
• B. ${28.4}^{0}C$
• C. ${65.8}^{0}C$
• D. ${72.4}^{0}C$

Answer 1

Answer: (C)

${65.8}^{0}C$

For the body to be floating with 0.98 of its body under water, the weight of the body would be supported by the buoyant force at that temperature.

$⟹Mg=0.98V{\rho }_{4^{\circ }C}g$

If weight of the body is supported by buoyant force when whole of the body is immersed,

$Mg=V{\rho }_{T^{\circ }C}g$

Hence, ${\rho }_{T^{\circ }C}=0.98{\rho }_{4^{\circ }C}$

But $\rho$ at some temperature T is given by $\frac{{\rho }_0}{1+\gamma \Delta T}$

Hence, $0.98=\frac{1}{1+\gamma (T-4)}$

Hence, $T={65.8}^{\circ }C$