Question

A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it extends by and when the weight is immersed completely in water, the extension is reduced to $l_w$.Then the relative density of the weight is

• A. $\frac{l_a}{l_w}$
  
• B. $\frac{l_a}{l_a-l_w}$
  
  
• C. $\frac{l_2}{l_a-l_w}$
  
• D. $\frac{l_w}{l_a}$
  

Answer 1

The correct option is B $\frac{l_a}{l_a-l_w}$



Case – 1 (in air)
$y=\frac{FL}{A\Delta l}=\frac{FL}{A{l}_a}\therefore F_{Thrust}=V\rho g$
$=\frac{V\rho gL}{A{l}_a}.....\left(1\right)$
Case – 2 when the load is immersed in a liquid,
$W_{net}=W_b-trust=V\rho g-V\times rh{o}_w\times g=V\rho g-V\times 1\times gY=\frac{(V\rho g-V\times 1\times g)L}{A{l}_w}.....\left(2\right)$
Y is same, because material is same (1) = (2),
We get
$\rho =\frac{l_a}{l_a-l_w}$