Question

A wire is suspended vertically from a rigid support. When loaded with a steel weight in air, the wire extends by $16cm$. When the weight is completely immersed in water, the extension is reduced to $14cm$. The relative density of the material of the weight is

• A. $2g/c{m}^3$
• B. $6g/c{m}^3$
• C. $8g/c{m}^3$
• D. $16g/c{m}^3$

Answer 1

The correct option is C $8g/c{m}^3$

$Y=\frac{Fl}{a△l};Y,l$ and $a$ are constants
$\therefore F=△l$
In the first csase, $V\rho g=16$
In the second case, $(V\rho g-V\times 1\times g)=14$
Dividing, $\frac{V_g(\rho -1)}{Vg\rho }=\frac{14}{16}=\frac{7}{8}$
or $\frac{\rho -1}{\rho }=\frac{7}{8}$ or $8\rho -7\rho$ or $\rho =8g/c{m}^3$.