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Properties of Matter

Section: Physics

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Question : 33 of 46

Marks: +1, -0

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertical 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

[JEE Adv 2012 P2]

more than half-filled if $\rho_c$ is less than 0.5.
more than half-filled if $\rho_c$ is more than 1.0.
half-filled if $\rho_c$ is more than 0.5.
less than half-filled if $\rho_c$ is less than 0.5.

Solution:

We have

\frac{V_m+V_a+V_w}{2} \rho_w g

=

V_m \rho_c \rho_w g + V_w \rho_w g

where

V_w

is the volume occupied by water in the shell,

V_a

is the volume occupied by air in the shell and

V_m

is the volume of the material in the shell.

V_w

=

V_m (1-2\rho_c) + V_a

If

\rho_c

>

\frac{1}{2}

, we get

V_w

<

V_a

.

If

\rho_c

<

\frac{1}{2}

, we get

V_w

<

V_a

.

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