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 o C such that its height above the water surface is 20 c m . When the temperature of water is increased to 4 o C , the height of the cylinder above the water surface becomes 21 c m . The density of water at T = 4 o C , relative to the density at T = 0 o C is close to:

Step-by-step solution

According to Archemedes Principle, weight of the body is balanced by the upward thrust force due to buoyancy. At 0 ° C , m g = A ( 100 - 20 ) ρ 0 ° C g , where A is area of cross-section of cylinder and ρ 0 ° C is density of water at 0 ° C . At 4 ° C , m g = A ( 100 - 21 ) ρ 4 ° C g , where ρ 4 ° C is density of water at 4 ° C . ρ 4 ° C ρ 0 ° C = 80 79 = 1.01