question_answer

A leak proof cylinder of length 1 m, made of a Metal which has very low coefficient of expansion is floating vertically in water at \[0{}^\circ C\]such that its height above the water surface is 20 cm. When the temperature of water is increased to \[4{}^\circ C,\] the height of the cylinder above the water surface becomes 21 cm. The density of water at \[T=4{}^\circ C,\]relative to the density at \[T=0{}^\circ C\]is close to [JEE MAIN Held On 08-01-2020 Morning]

A)  1.04    

B)       1.03

C)  1.26                

D)     

1.01 Correct Answer: D Solution :

[d] Law of floatation

\[\frac{{{V}_{i}}}{V}=\frac{{{\rho }_{body}}}{{{\rho }_{liquid}}}\]

In given case

\[\therefore \frac{{{h}_{1}}}{{{h}_{2}}}=\frac{\left( {{\rho }_{4{}^\circ c}} \right)}{\left( {{\rho }_{0{}^\circ c}} \right)}\left[ {{\rho }_{body}}=\text{constant} \right]\]

\[\frac{{{p}_{4{}^\circ c}}}{{{p}_{0{}^\circ c}}}\left( \frac{100-20}{100-21} \right)=\frac{80}{79}=1.01\]