Question

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

• A. Buoyancy will be less in water at $0^{o}C$ than that in water at $4^{o}C$.
• B. Buoyancy will be more in water at $0^{o}C$ than that in water at $4^{o}C$.
• C. Buoyancy in water at $0^{o}C$ will be same as that in water $4^{o}C$.
• D. Buoyancy may be more or less in water at $4^o$ depending on the radius of the sphere.

Answer 1

Answer: (A)

Buoyancy will be less in water at $0^{o}C$ than that in water at $4^{o}C$.

As buoyancy at $0^{o}C,F_b=V{\rho }_{0}g$ and buoyancy at $4^{o}C,F_b^{\prime }=V{\rho }_{4}g$
$\frac{F_b}{F_b^{\prime }}=\frac{{\rho }_0}{{\rho }_4}<1$(density of water at $4^{o}C$ is maximum)
i.e., $F_b<F_b^{\prime }$