Question

A metallic block weighs $15N$ in air. It weighs $12N$ when immersed in water and $13N$ when immersed in another liquid. What is the specific gravity of the liquid?

• A. $12/13$
• B. $1/3$
• C. $13/15$
• D. $2/3$

Answer 1

The correct option is D $2/3$

Weight in air,
$V{p}_{b}g=15\dots \left(i\right)$

Weight in water,
$V{p}_{b}g-V{p}_{w}g=12\dots \left(ii\right)$

Weight in liquid,
$V{p}_{b}g-V{p}_{l}g=13\dots \left(iii\right)$

From equation $\left(i\right)$ and $\left(ii\right)$,

$\frac{p_b}{p_w}=\frac{15}{15-12}\dots \left(iv\right)$

From equation $\left(i\right)$ and $\left(iii\right)$,

$\frac{p_b}{p_l}=\frac{15}{15-13}\dots \left(v\right)$

Solving $\left(iv\right)$ and $\left(v\right)$,

$\frac{p_l}{p_w}=\frac{2}{3}$