JEE PYQ: Mechanical Properties Of Fluids Question 19
Question 19 - 2020 (08 Jan 2020 Shift 1)
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:
(1) 1.26
(2) 1.04
(3) 1.01
(4) 1.03
Show Answer
Answer: (3) 1.01
Solution
When cylinder is floating in water at 0$^\circ$C: Net thrust $= A(h_2 - h_1)\rho_{0^\circ C} g = A(100 - 80)\rho_{0^\circ C} g$ When cylinder is floating in water at 4$^\circ$C: Net thrust $= A(h_2 - h_1)\rho_{4^\circ C} g = A(100 - 21)\rho_{4^\circ C} g$ $\therefore \frac{\rho_{4^\circ C}}{\rho_{0^\circ C}} = \frac{80}{79} = 1.01$
BETA
