Q. A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_{c}$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
A) More than half filled if $\rho_{c}$ is less then 0.5
B) More than half filled if $\rho_{c}$ is less then 1.0
C) Half filled if $\rho_{c}$ is less then 0.5
D) Less than half filled if $\rho_{c}$ is less then 0.5
Explanation
(d) $mg + \rho \times V_{\mathcal{l}} \times g = \frac{V_{0}}{2} \times \rho \times g$
$V_{\mathcal{l}} = \frac{V_{0}}{2} - \frac{m}{\rho}$
So $V_{\mathcal{l}} < \frac{V_{0}}{2}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.