Q. Wires $A$ and $B$ are made from the same material. A has twice the diameter and three times the length of $B$. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ is
A) 2 : 3
B) 3 : 4
C) 3 : 2
D) 6 : 1
Explanation
(b) $U = \frac{1}{2}Fl = \frac{F^{2}L}{2AY}.\ U \propto \frac{L}{r^{2}}\ \lbrack F$ and $Y$ are constant]
$\therefore\frac{U_{A}}{U_{B}} = \left( \frac{L_{A}}{L_{B}} \right) \times \left( \frac{r_{B}}{r_{A}} \right)^{2} = (3) \times \left( \frac{1}{2} \right)^{2} = \frac{3}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.