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

For solid P,
Let `V_(P)` and `rho p` be volume and density of solid respectively.

As the solid P is floting in water,
`:.` Water of P = weight of water displaced by P
`V_(P) rho_(P) g = (V_(P))/(2) rho_("water")g`
`rho_(P) = (1)/(2) rho_("water")`...(i)
Similarly, for solid Q

`V_(Q) rho_(Q) g= (2)/(3) V_(Q) rho_("water")g`
`rho_(Q) = (2)/(3) rho_("water")` ...(ii)
Divide (i) by (ii), we get
`(rho_(P))/(rho_(Q)) = (3)/(4)`