Two solids P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with `(2^(rd))/(3)` of its volume is immersed. The ratio of densities of P and Q is

Options

A. `4//3`
B. `3//4`
C. `2//3`
D. `3//2`

Answer

B

Explanation

According to law of floatation
wt. of body = wt of water displaced for body P.
`v_(p)p_(p).g=(V_(P))/2p_(w).grArrp_(P)=(p_(w))/2`
For body Q.
`V_(Q)p_(Q).g=2/3V_(Q).p_(w)grArrp_(Q)=2/3p_(w)`
`therefore(p_(P))/(p_(Q))=((p_(w))/2)(2/3p_(w))=3/4`
So correct choice is (b).