A wire 2m in length suspended vertically by 10mm when the mass of 10kg is attached to the lower end. The elastic potential energy gain by the wire is?
(Take g =$10m/{s^2}$ )
A. 0.5 J
B. 5 J
C. 50 J
D. 500 J

Hint: According to Hooke’s law the force required to stretch the spring is directly proportional to the amount of stretch. Therefore the elastic potential energy is that potential energy which stored the result of the deformation of elastic objects for example stretching the string.

Complete answer:
According to this given question:
Where, spring force by wire = weight of mass attached
$
  k\Delta x = mg \\
  \Rightarrow k(0.001) = 10 \times 9.8 \\
  \Rightarrow k = 9800N/m \\
$
Now, elastic potential energy:
$
  {\text{U = (0}}{\text{.5)k}}\Delta {{\text{x}}^2} \\
   \Rightarrow (0.5) \times 9800 \times {(0.01)^2} \\
  \therefore U = 0.49 \approx 0.5J \\
$

So, the correct answer is “Option A”.

Additional Information:
The stored energy that is converted into kinetic energy is known as potential energy. There are five types of potential energy chemical potential energy, electrical potential energy, magnetic potential energy and elastic potential energy, gravitational potential energy. The term potential meaning is different from the term potential energy; potential means the ability of an object to do some work whereas potential energy means the amount of energy which is acquired due to that potential difference.
Some of the examples given below will make you understand potential energy easily.

a.)A kid on a top of slide
b.)A car which is parked on the top of the hill
c.)A play toy yoyo, before it is released
d.)A book on shell before it falls

Note:
As we studied from starting that energy neither be created nor be destroyed. However, the potential and kinetic energy are very different in nature i.e., the energy in a body due to its position is said to be potential energy and the energy in a body due to its motion is said to be kinetic energy.