A) 30%
B) 50%
C) 60%
D) 67%
Correct Answer: B
Solution :
Let densities of wood and liquid are \[{{\rho }_{w}}\]and \[{{\rho }_{l}}\]respectively. When vessel is stationary weight = upthrust ie, \[V{{\rho }_{w}}g={{V}_{l}}{{\rho }_{l}}g\] or \[\frac{{{V}_{l}}}{V}=\frac{{{\rho }_{w}}}{{{\rho }_{l}}}\] ?(i) When the vessel moves upwards with acceleration g/3. upthrust - weight = mass \[\times \] acceleration \[{{V}_{l}}{{\rho }_{l}}\left( g+\frac{g}{3} \right)-V{{\rho }_{w}}g=V{{\rho }_{w}}\times \frac{g}{3}\] \[\frac{{{V}_{1}}}{V}=\frac{{{\rho }_{w}}}{{{\rho }_{l}}}\] ?(ii) From Eqs. (i) and (ii), we note that \[\frac{{{V}_{l}}}{V}=\frac{{{V}_{l}}}{V}\] ie, fraction of volume immersed in liquid remains unchanged.
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