JEE MAIN - Physics (2020 - 8th January Morning Slot - No. 17)
A leak proof cylinder of length 1m, made of
a metal which has very low coefficient of
expansion is floating vertically in water at 0°C
such that its height above the water surface is
20 cm. When the temperature of water is
increased to 4°C, the height of the cylinder
above the water surface becomes 21 cm. The
density of water at T = 4°C, relative to the
density at T = 0°C is close to :
1.04
1.26
1.01
1.03
Explanation
In both cases weight of the cylinder is balanced by buoyant force exerted by liquid.
Case - 1 : $${\rho _{0^\circ C}}\left( {100 - 20} \right) \times g$$ = mg
Case - 2 : $${\rho _{4^\circ C}}\left( {100 - 21} \right) \times g$$ = mg
$$ \therefore $$ $${{{\rho _{4^\circ C}}\left( {100 - 21} \right)} \over {{\rho _{0^\circ C}}\left( {100 - 20} \right)}}$$ =1
$$ \Rightarrow $$ $${{{\rho _{4^\circ C}}} \over {{\rho _{0^\circ C}}}}$$ = $${{80} \over {79}}$$ = 1.01
Case - 1 : $${\rho _{0^\circ C}}\left( {100 - 20} \right) \times g$$ = mg
Case - 2 : $${\rho _{4^\circ C}}\left( {100 - 21} \right) \times g$$ = mg
$$ \therefore $$ $${{{\rho _{4^\circ C}}\left( {100 - 21} \right)} \over {{\rho _{0^\circ C}}\left( {100 - 20} \right)}}$$ =1
$$ \Rightarrow $$ $${{{\rho _{4^\circ C}}} \over {{\rho _{0^\circ C}}}}$$ = $${{80} \over {79}}$$ = 1.01
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