A certain block weighs 15 N in air. But is weighs only 12 N when completely immersed in water. When immersed completely in another liquid, it weighs 13 N. Calculate the relative density of (i) the block and (ii) the liquid.

Options

A. `(15)/(2)`
B. `15`
C. `(15)/(4)`
D. `(13)/(12)`

Answer

A

Explanation

`rho_(b) vg = 15` ….(i)
`rho_(b) vg - rhp_(w) vg = 12` …..(ii)
`rho_(b)vg - rho_(l)vg = 13` ….(iii)
From (i) and (iii)
`3 = rho_(w)vg`
`rArr vg = 3 xx 10^(-3)`
`rho_(b) = (15)/(3 xx 10^(-3)) = 5xx 10^(3)`
`rho_(l)vg = 2`
`rho_(l) = (2)/(3 xx 10^(-3)) = (2)/(3) xx 10^(3)`
`(rho_(b))/(rho_(l)) = (15)/(2)`