Question

A wooden block is floating in a liquid 50% of volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration a=g/3 is

• A. $30$%
• B. $50$%
• C. $60$%
• D. $67$%

Answer 1

Answer: (D)

$67$%

weight of the block = Buoyant force by liquid

${\rho }_{b}Vg={\rho }_l\frac{v}{2}g$

$\frac{{\rho }_b}{{\rho }_l}=\frac{1}{2}$

when its moving ,let the buoyancy force be F

$F-{\rho }_{b}Vg=\frac{{\rho }_{b}Vg}{3}$

$F=\frac{4{\rho }_{b}Vg}{3}$

Also$F={\rho }_l{V}^{\prime }g=\frac{4{\rho }_{b}Vg}{3}$

$V^{\prime }=\frac{2}{3}V$