Question

One end of a horizontal thick copper wire of length $2L$ and radius $2R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

• A. $0.25$
• B. $0.50$
• C. $2.00$
• D. $4.00$

Answer 1

The Correct Option is C

Both the rods are made up of same kind of material, i.e. their young?? modulus is same. $K_{1}$ $=\frac{\pi4R^{2}Y}{2L}$, $k_{2}$ $=\frac{\pi R^{2}Y}{L}$ Force constants of two rods are, $\therefore$ $\quad$ $F=k_{1}x$$=k_{2}Y$ $\Rightarrow$$\quad$ $\frac{y}{x}=\frac{k_{1}}{k_{2}}=2$