A) \[y=\frac{{{\rho }_{b}}}{{{\rho }_{\ell }}}\]
B) \[\frac{3}{8}\]
C) \[\frac{2}{3}\]
D) \[\frac{3}{4}\]
Correct Answer: A
Solution :
[a] Let 'x' fraction of volume immersed in first case and y fraction in second case 1st case W = upthrust \[V{{\rho }_{b}}g=(xV){{\rho }_{\ell }}g\] \[x=\frac{{{\rho }_{b}}}{{{\rho }_{\ell }}}\] 2nd case upthrust - Weight = ma \[(yV){{\rho }_{\ell }}\left[ g+\frac{g}{3} \right]-V{{\rho }_{b}}g={{V}_{{{\rho }_{b}}}}\frac{g}{3}\] \[y=\frac{{{\rho }_{b}}}{{{\rho }_{\ell }}}\] It is independent of acceleration due to gravity
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