Question

A certain block weights $15N$ in air. It weighs $12N$ when immersed in water. When immersed in another liquid, it weighs $13N.$ The relative density of the block and the other liquid are respectively:

• A. $5,\frac{2}{3}$
• B. $\frac{2}{3},5$
• C. $\frac{4}{5},5$
• D. $5,\frac{4}{5}$

Answer 1

Answer: (A)

$5,\frac{2}{3}$

Upthrust acting on the block in water $=15N-12N=3N$ = ( volume of solid immersed )( density of liquid ) g = V (1) 10 where V is the volume of the block , so $V=\frac{3}{10}=0.3$ $c{m}^3$

Block weighs $15N$ in air implies $15=mg$ , implies $m=\frac{15}{10}=1.5g$

now density = $\frac{mass}{volume}$ = $\frac{1.5}{0.3}$ = 5 $g/c{m}^3$

so density of block = 5 $g/c{m}^3$

hence , relative density of the block = density of block / density of water$=\frac{5}{1}=5$

now Upthrust acting on the block in the liquid $=15N-13N=2N=$ (volume of solid immersed ) ( density of liquid ) $g=V\rho g=0.3$( $\rho )g$ ,

implies $\rho$ of the liquid $=\frac{2}{3}g/c{m}^3$

so relative density of the liquid = density of liquid / density of water = $\frac{2}{\frac{3}{1}}=\frac{2}{3}$

so option (A) is correct