Question

Two spheres of different materials immersed in water experience equal up thrust, both the spheres have equal ________ .

• A. weights in air
• B. densities
• C. volumes
• D. mass

Answer 1

The correct option is C

volumes

According to archimedes principle up thrust is equal to the weight of the fluids displaced by the object weight in the fluid
$$\begin{gathered} \mathrm{upthrust}=\mathrm{volume}\mathrm{of}\mathrm{fluid}\mathrm{displaced}\times \mathrm{density}\times \mathrm{acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity} \\ \mathrm{given}\mathrm{that}\mathrm{the}\mathrm{spheres}\mathrm{experience}\mathrm{equal}\mathrm{thrust} \\ {\mathrm{V}}_1\mathrm{\rho g}={\mathrm{V}}_2\mathrm{\rho g} \\ \Rightarrow {\mathrm{V}}_1={\mathrm{V}}_2 \\ \mathrm{Thus}\mathrm{upthrust}\mathrm{of}\mathrm{two}\mathrm{different}\mathrm{sphers}\mathrm{must}\mathrm{have}\mathrm{equal}\mathrm{volume}\mathrm{though}\mathrm{made}\mathrm{of}\mathrm{different}\mathrm{materials} \end{gathered}$$

Hence option (c) is the correct answer.