Potential Energy

To find the inductance, we use the formula for energy stored in an inductor:

Given:

Substitution:

Final Answer:

To determine the elastic potential energy stored in the extended wire when a block of mass is suspended, we need to consider the properties of the wire and the forces involved.

The wire extends from its original length to , showing an elongation of . The tensile force causing this elongation is due to the weight of the block, which is , where is the acceleration due to gravity.

The formula for elastic potential energy ( ) stored in a wire or spring due to elongation is:

U = \frac{1}{2} \times \text{Force} \times \text{Elongation}

Here, the force involved is the weight of the block, , and the elongation is . Therefore, the formula for the elastic potential energy becomes:

U = \frac{1}{2} \times Mg \times l

This calculation shows that the elastic potential energy stored in the wire is indeed .

Thus, the correct option is:

Justification for Other Options:

• Mgl : This value would imply that the entire energy is transferred directly to elongation without respecting the energy distribution stored in the wire, according to principles of elasticity.
• MgL : This would imply that the wire entirely stretches by its own length , which is not the case here.
• : This implies elasticity involving the whole initial length , which isn’t appropriate in the context of merely considering elongation .

Hence, with a step-by-step analysis, the elastic potential energy is determined correctly as .