Question

A wire of radius $r$, Youngs modulus $Y$ and length $l$ is hung from a fixed point and supports a heavy metal cylinder of volume $V$ at its lower end. The change in length of wire when cylinder is immersed in a liquid of density $\rho$ is in fact

• A. decreases by$\frac{Vl\rho g}{Y\pi r^2}$
• B. increases by$\frac{Vr\rho g}{Y\pi l^2}$
• C. decreases by$\frac{V\rho g}{Y\pi r}$
• D. increases by$\frac{V\rho g}{\pi rl}$

Answer 1

The correct option is A decreases by$\frac{Vl\rho g}{Y\pi r^2}$

$Y=\frac{F/A}{△l/l}$

$△l=\frac{Fl}{AY}$

$△l_1=\frac{(F-F_B)l}{AY}$

So, change in length is

$△l-△l_1=\frac{F_{B}l}{AY}$

$=\frac{PVgl}{AY}=\frac{PVgl}{Y\pi r^2}(\because F_B=VPg)$

length decreases because bouyant force acts in upward direction, So, tension decreases, so length also decreases.