A) \[\frac{5}{3}\]
B) \[\frac{4}{3}\]
C) \[\frac{3}{2}\]
D) 1
Correct Answer: B
Solution :
[b]: When the body is floating in a liquid, then Weight of the body = Weight of liquid displaced i.e.\[{{V}_{body}}{{\rho }_{body}}g={{V}_{inside}}{{\rho }_{liquid}}g\] Let V be the volume of the body. In water, \[V{{\rho }_{body}}g=\frac{2}{3}{{\rho }_{water}}g\] \[{{\rho }_{body}}=\frac{2}{3}{{\rho }_{water}}\] ....(i) In oil,\[V{{\rho }_{body}}g=\frac{1}{2}V{{\rho }_{oil}}g\] \[{{\rho }_{body}}=\frac{1}{2}{{\rho }_{oil}}\] ....(ii) From (i) and (ii) we get\[\frac{{{\rho }_{oil}}}{{{\rho }_{water}}}=\frac{4}{3}\] Specific gravity of oil\[\frac{{{\rho }_{oil}}}{{{\rho }_{water}}}=\frac{4}{3}\]
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