A leak proof cylinder of length 1m, made of a metal which has very… | JEE Main 2020 (8 Jan, Shift 1)

Q16JEE Main 2020 · 8 JAN · SHIFT 1Medium

Archimedes' Principle & Floatation

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:

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Answer: (c)

Weight is constant, so $\rho\,h_{sub}$ = constant (same cross-section).
Submerged length: $100 - 20 = 80$ cm at $0^\circ$ C, $100 - 21 = 79$ cm at $4^\circ$ C.
$\rho_0 \times 80 = \rho_4 \times 79 \Rightarrow \dfrac{\rho_4}{\rho_0} = \dfrac{80}{79} \approx 1.013$
So the answer is (c) 1.01.

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