Verified Solution • 2025–26 Session moderate

QJEEM20Ph52ff: JEE Main 2020 Physics - Class 11 JEEM20Ph52ff Solution: A leak proof cylinder of length 1m, made of a metal which has…

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 :

Multiple Choice Options

  • A 1.04
  • B 1.26
  • C 1.01
  • D 1.03

Step-by-Step Verified Solution

In both cases weight of the cylinder is balanced by buoyant force exerted by liquid.

Case - 1 : ρ0∘C(100−20)×g{\rho _{0^\circ C}}\left( {100 - 20} \right) \times g = mg

Case - 2 : ρ4∘C(100−21)×g{\rho _{4^\circ C}}\left( {100 - 21} \right) \times g = mg

∴\therefore ρ4∘C(100−21)ρ0∘C(100−20){{{\rho _{4^\circ C}}\left( {100 - 21} \right)} \over {{\rho _{0^\circ C}}\left( {100 - 20} \right)}} =1

⇒\Rightarrow ρ4∘Cρ0∘C{{{\rho _{4^\circ C}}} \over {{\rho _{0^\circ C}}}} = 8079{{80} \over {79}} = 1.01

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