A wire of natural length l, Youngs modulus Y and area of cross-section A is extended by x . Then the energy stored in the wire is given by

Question

A wire of natural length l, Youngs modulus Y and area of cross-section A is extended by x . Then the energy stored in the wire is given by (A)  (1/2)(YA/l)x2  (B)  (1/3)(YA/l)x2  (C)  (1/2)(Yl/A)x2  (D)  (1/2)(YA/l2)x2

Tardigrade Admin · Accepted Answer

Energy stored in the wire U=(1/2)Y× (strain)2× volume Or U=(1/2)Y× ( (x/l) )2× Al Or U=(1/2)(Yx2/l)× A Or U=(1/2)(YA/l)x2

Q. A wire of natural length $l,$ Youngs modulus $Y$ and area of cross-section $A$ is extended by $x$ . Then the energy stored in the wire is given by

$\frac{1}{2} \frac{Y A}{l} x^{2}$

$\frac{1}{3} \frac{Y A}{l} x^{2}$

$\frac{1}{2} \frac{Y l}{A} x^{2}$

$\frac{1}{2} \frac{Y A}{l ^{2}} x^{2}$

$\frac{1}{2} \frac{A}{Y l} x^{2}$

Energy stored in the wire
$U = \frac{1}{2} Y \times (s t r ain)^{2} \times v o l u m e$
Or $U = \frac{1}{2} Y \times (\frac{x}{l})^{2} \times A l$
Or $U = \frac{1}{2} \frac{Y x ^{2}}{l} \times A$
Or $U = \frac{1}{2} \frac{Y A}{l} x^{2}$

Q. A wire of natural length l, Youngs modulus Y and area of cross-section A is extended by x . Then the energy stored in the wire is given by

21​lYA​x2

31​lYA​x2

21​AYl​x2

21​l2YA​x2

21​YlA​x2

Energy stored in the wire U=21​Y×(strain)2×volume Or U=21​Y×(lx​)2×Al Or U=21​lYx2​×A Or U=21​lYA​x2