Explanation:

When a block of mass M is suspended by a long wire of length L, the wire undergoes extension due to the weight of the block. Let's analyze the situation in detail.

1. Definition of Elastic Potential Energy:

Elastic potential energy is the energy stored in an object when it is stretched or compressed. It is given by the formula:

Elastic Potential Energy (PE) = 1/2 k x^2

Where:
- PE is the elastic potential energy
- k is the spring constant
- x is the extension or compression of the spring

2. Extension of the Wire:

In this scenario, the wire is acting like a spring. When the block is suspended, the weight of the block causes the wire to extend. Let's assume the extension of the wire is 'l'.

3. Calculation of Elastic Potential Energy:

To calculate the elastic potential energy stored in the extended wire, we need to determine the spring constant of the wire.

The spring constant (k) can be determined using Hooke's Law, which states that the force required to extend or compress a spring is directly proportional to the extension or compression.

Hooke's Law: F = kx

Where:
- F is the force applied
- k is the spring constant
- x is the extension or compression of the spring

In this scenario, the force applied is the weight of the block, which is equal to Mg (mass x acceleration due to gravity).

Therefore, Mg = k * l

Solving for k, we get k = Mg / l

Now, we can substitute the value of k into the formula for elastic potential energy:

PE = 1/2 * (Mg / l) * l^2

Simplifying, we get PE = 1/2 * Mg * l

4. Conclusion:

Therefore, the elastic potential energy stored in the extended wire is given by the expression 1/2 * Mg * l. So, the correct answer is option (c) 1/2MgL.