An alminium sphere is dipped into water. Which of the following is true ?

Options

A. Buoyancy will be less in water at `0^(@)C` than that in water at `4^(@)C`
B. Buoyancy will be more in water at `0^(@)C` than that in water at `4^(@)C`
C. Buoyancy in water at `0^(@)C` will be same as that in water at `4^(@)C`
D. Buoyancy may be more or less in water at `4^(@)C` depending on the radius of the shpere.

Answer

A

Explanation

Let a volume of the sphere is V and `rho` is the its density, then we can write buoyant force
`F = V rho G` (g = acceleration due to gravity)
`rArr F prop rho` (`because` V and g are almost constant)
`rArr (F_(4^(@)C))/(F_(0^(@)C))= (rho_(4^(@)C))/(rho_(0^(@)C)) gt 1 " " (because rho_(4^(@)C) gt rho_(0^(@)C))`
`rArr (F_(4^(@)C) gt F_(0^(@)C))`
Hence, buoyancy will be less in water at `0^(@)C` than that in water at `4^(@)C`.