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

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