Question

A boat is floating in water at 0${}^0$C such that 97% of the volume of the boat is submerged in water. The temperature at which the boat will just completely sink in water is $({\gamma }_R=3\times {10}^{-4}{/}^{o}C)$

• A. ${10}^{0}C$
• B. ${100}^{0}C$
• C. ${60}^{0}C$
• D. ${50}^{0}C$

Answer 1

The correct option is B ${100}^{0}C$

In equilibrium, upward thrust = weight of the body
$UpwardThrust=V_{boat-submerged}\times d_0\times g=\frac{97}{100}\times V_{boat}\times d_0\times g$
At temp t the boat is completely submerged.
$(Thrust{)}_t=V_{boat-submerged}\times d_t\times g=V_{boat}\times d_t\times g$
$(Thrust{)}_0=(Thrust{)}_t$
$\Rightarrow \frac{97}{100}\times d_0=d_t=d_0(1-{\gamma }_r\ast t)$
$\Rightarrow {\gamma }_r\times t=1-\frac{97}{100}$
$\Rightarrow 3\times {10}^{-4}\times t=3\times {10}^{-2}$
$\Rightarrow t=100$