Question

A solid block of density ${\rho }_S$ is immersed in a liquid of density ${\rho }_L$, and it floats half submerged in the liquid. What is the apparent weight of the solid? (Given: True weight of the solid $=W$)

• A. $W(1-\frac{2{\rho }_L}{{\rho }_S})$
• B. $W(1-\frac{{\rho }_L}{2{\rho }_S})$
• C. $W(1-\frac{{\rho }_L}{{\rho }_S})$
• D. $W(2-\frac{{\rho }_L}{{\rho }_S})$

Answer 1

The correct option is B $W(1-\frac{{\rho }_L}{2{\rho }_S})$

Apparent weight = True weight – Upthrust
True weight $=W$
Upthrust = (Volume submerged) $\times$ (Density of liquid) $\times$ g
Apparent weight $=W–(\frac{1}{2}\times \frac{W}{{\rho }_{S}g})\times \left({\rho }_L\right)\times g$
Apparent weight $=W(1-\frac{{\rho }_L}{2{\rho }_S})$