Question

A wire suspended from one end carries a sphere at its other end. The elongation in the wire reduces from $2mm$ to $1.6mm$ on completely immersing the sphere in water. The density of the material of the sphere is

• A. 3200 kg/m${}^3$
• B. 800 kg/m${}^3$
• C. 1250 kg/m${}^3$
• D. 5000 kg/m${}^3$

Answer 1

The correct option is D 5000 kg/m${}^3$

$Y=\frac{F/A}{△L/L}$
$Y=\frac{F_1/A}{2/L}=\frac{F_2/A}{1.6/L}$
$\frac{4}{5}{F}_1=F_2$
Bouyant force $=F_1-F_2=\frac{F_1}{5}$
$F_1={\rho }_s{V}_{s}g$
Bouyant force $={\rho }_w{V}_{s}g=\frac{F_1}{5}$
$\Rightarrow 5{\rho }_w{V}_{s}g={\rho }_s{V}_{s}g$
$\Rightarrow {\rho }_s=5{\rho }_w$
$\Rightarrow {\rho }_s=5000kg/m^3(\because {\rho }_w=1000kg/m^3)$
So, density of material is $5000kg/m^3$