First slide

Elastic Modulie

Question

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

Moderate

A

2 : 3
B

3 : 4
C

3 : 2
D

6 : 1

Solution

$\begin{array}{l} U = \frac{1}{2} FI = \frac{F^{2} L}{2 AY} \cdot U \propto \frac{L}{r^{2}} [Fand Y are constant] \\ ∴ \frac{U_{A}}{U_{B}} = (\frac{L_{A}}{L_{B}}) \times {(\frac{r_{B}}{r_{A}})}^{2} = (3) \times {(\frac{1}{2})}^{2} = \frac{3}{4} . \end{array}$

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