Question

If in a wire of Young’s modulus Y, longitudinal strain X is produced, then
the value of potential energy stored in its unit volume will be
(a) Y X² (b) 2 Y X²
(c) Y² X/2 (d) Y X²/2

Answer 1

Solution

Option (D) is correct

Given

• Young's Modulus is Y

• Strain produced is X

To finD

Elastic Potential Energy

Elastic Potential Energy in a spring is given as :

$\tt U = \dfrac{1}{2} \times Stress \times Strain$

Now,

$\tt Y = \dfrac{Stress}{Strain} \\ \\ \longrightarrow \tt Stress = Y \times Strain$

Therefore,

$\dashrightarrow \tt U = \dfrac{1}{2} \times (Y \times Strain) \times Strain$

• Strain Produced here is X

Thus,

$\dashrightarrow \large{\boxed{\boxed{\tt U = \dfrac{X^2Y}{2}}}}$

Answer 2

Answer:

d. is the right answer

hope it is right