Question

A beaker with a liquid of density $1.4gc{m}^{-3}$ is in balance over one pan of a weighing machine. If a solid of mass $10g$ and density $8gc{m}^{-3}$ is now hung from the top of that pan with a thread and sinking fully in the liquid without touching the bottom, the extra weight to be put on the other pan for balance will be

• A. $10.0g$
• B. $8.25g$
• C. $11.75g$
• D. $-1.75g$

Answer 1

The correct option is A $10.0g$

Volume of solid object $V=mass/density=10/8c{m}^3$

Buoyancy force =$V\rho g=1.75g$

Thrust due to Buoyancy $=1.75g$.

Tension on string $=10g-1.75=8.25g$

Extra weight$=8.25g+1.75g=10g$