Question

Q]There is a leak proof cylinder of length 1 m, made of a metal that 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.
If the temperature of water is increased to 4° C, the height f 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 approximately.​

Answer 1

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1.01

Let A be the area of cross section of the cylinder.

p0 be the density of water at 0oC

p4 be the density of water at 4oC.

Total length of the cylinder is 100cm

Given that the length of the cylinder above the surface of water is 20cm

At 0oC, the weight of the cylinder is balanced by the buoyant force.

p0A×0.8×g=w      [Buoyant force =pAlg]    ...(i)

At 4^oC$$, thef weight of the cylinder is balanced by the buoyant force.

p4A×0.79×g=w    ...(ii)

Dividing (i) by (ii)

p4×0.79p0×0.8=1, p4=0.79p0×0.8=0.012p0

p0p4=1.012≃1.01

Answer 2

Answer:

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ᵃⁿˢʷᵉʳシ︎

1.01

Let A be the area of cross section of the cylinder.

p0 be the density of water at 0oC

p4 be the density of water at 4oC.

Total length of the cylinder is 100cm

Given that the length of the cylinder above the surface of water is 20cm

At 0oC, the weight of the cylinder is balanced by the buoyant force.

p0A×0.8×g=w [Buoyant force =pAlg] ...(i)

At 4^oC, thef weight of the cylinder is balanced by the buoyant force.

p4A×0.79×g=w ...(ii)

Dividing (i) by (ii)

p4×0.79p0×0.8=1, p4=0.79p0×0.8=0.012p0

p0p4=1.012≃1.01