An aluminium 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 sphere.

Answer

A

Explanation

Suppose volume of sphere is V and its density is `sigma` and density of water is `rho`
`:.` Mass of sphere `m=Vrho`
Bouyant force `F=mg`
`F=Vrhog" "[becausem=Vxxrho]`
`Fprop rho" "[because" V and "rho" are constant"]`
`:.(F_(4^(@)C))/(F_(0^(@)C))=(rho_(4^(@)C))/(rho_(0^(@)C))`
But density of `4^(@)C` temperature water is maximum,
`:.rho_(4^(@)C)gtrho_(0^(@)C)rArr(rho_(4^(@)C))/(rho_(0^(@)C))gt1`
`:.F_(4^(@)C)/(F_(0^(@)C))gt`
`:.F_(4^(@)C)gtF_(0^(@)C)`
Hence, Buoyant force in `0^(@)C` water is less than that in `4^(@)C`.