Question

If a sample of metal weighs $210gm$ in air, $180gm$ in water and $120gm$ in a liquid. Then the:

• A. relative density of metal is $3$
• B. relative density of metal is $7$
• C. relative density of liquid is 1010
• D. relative density of liquid is $\left(1/3\right)$

Answer 1

Answer: (B)

relative density of metal is $7$

Neglacting uptherst exerted by air,
True mass of metal$=210gm$
Mass of metal in water $=180gm$
Loss in mass/upthrust $=30gm$
$\therefore$ Volume of liqiud displaced / volume of metal = $30c{m}^3$
So, Density of metal = $\frac{210}{30}g/c{m}^3=7g/c{m}^3$
In the fluid,
Loss of mass of block $90gm$
Volume of fluid displaced = $30c{m}^3$
$\therefore$ Density of fluid $=\frac{90}{30}g/c{m}^3=3g/c{m}^3$
So,
R.D of metal$=7$
R.D of fluid$=3$