Question

When a load of \[10\,{\text{kg}}\]is hung from the wire, then extension of \[{\text{2 m}}\] is produced. Then work done by restoring force is
A. \[{\text{200 J}}\]
B. \[{\text{100 J}}\]
C. \[{\text{50 J}}\]
D. \[{\text{25 J}}\]

Answer 1

Hint:To find the work done by the restoring force, first you will need to find the value of force constant of the wire. To find the value of force constant you will need to balance the weight of the load and the restoring force. After that, put the value of force constant in the formula of work done to get the required answer.

Complete step by step answer:
Given, load hung from the wire, \[m = 10\,{\text{kg}}\].
Extension or displacement of wire produced, \[x = {\text{2 m}}\].
Let the acceleration due to gravity be \[g = 10\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}\].
We have the formula for restoring force as,
\[F = kx\] (i)
where \[k\] is the force constant and \[x\] is the displacement of the wire.
Here, the displacement is \[x = {\text{2 m}}\] so, the restoring force of the wire will be,
\[F = k \times 2\]
\[ \Rightarrow F = 2k\]
The weight of the load will balance this restoring force that is,
\[F = {\text{weight of the load}}\] (ii)
We have the formula for weight of a object as,
\[W = mg\]
Putting this value in equation (ii) we get,
\[F = mg\]
Putting the values of \[F\], \[m\] and \[g\] we get,
\[2k = 10 \times 10\]
\[ \Rightarrow k = \dfrac{{100}}{2}\]
\[ \Rightarrow k = 50\,{\text{N}}{{\text{m}}^{{\text{ - 1}}}}\]
 Work done by restoring force is given by the formula,
\[W = \dfrac{1}{2}k{x^2}\]
Putting the value of \[k\] and \[x\] in the above formula we get,
\[W = \dfrac{1}{2} \times 50 \times {2^2}\]
\[ \Rightarrow W = 50 \times 2\]
\[ \therefore W = 100\,{\text{J}}\]
Therefore, work done by restoring force is \[100\,{\text{J}}\].

Hence, the correct answer is option B.

Note:Restoring force is the force which brings a body back to its original size and shape. The restoring force given by Hooke’s law which states that force needed to extend or compress a wire or spring is directly proportional to the displacement from its mean position. There is also another term known as deforming force, which is the force that changes the size and shape of a body.