A cylinder of height 1m is floating in water at `0^(@)C` with 20cm height in air. Now the temperature of water is raised to `4^(@)C`, the height of the cylinder in air becomes 21cm. The ratio of density of water at `4^(@)C` to that at `0^(@)C` is (Consider expansion of the cylinder is negligible)

Options

A. 1.01
B. 1.03
C. 1.04
D. 2.01

Answer

A

Explanation

As cylinder floats in water, buoyant force balances weight

`:. mg= A L rho g`
where L= length of cylinder in water
m,g, A are same
`:. L rho`= constant
`:. L_(4) rho_(4)= L_(0) rho_(0)`
`:. (rho_(4))/(rho_(0)) = (L_(0))/(L_(4)) = ((100-20))/((100-21))`
`:. (rho_(4))/(rho_(0)) = (80)/(79) = 1.01265`
`:. (rho_(4))/(rho_(0))= 1.01`