Question

If the potential energy of the spring is V and upon stretching it by 2 cm then its potential energy when it is stretched by 10 cm will be?
A. \[\dfrac{V}{25}\]
B. 5 V
C. \[\dfrac{V}{5}\]
D. 25 V

Answer 1

Hint: We are given this problem in the spring and had to solve for its potential energy. We know spring has a spring of force constant, and it has the tendency to return to its equilibrium position that is the unstretched position when it is either compressed or stretched. The energy possessed by the spring when it is either stretched or compressed is called its potential energy.

Complete step by step answer:
We know potential energy of the spring is given by the formula, \[U=\dfrac{k{{x}^{2}}}{2}\], where k is the spring constant of the spring in units of N/m and x is the displacement of the spring from its equilibrium position in units of metres.
Now as per the question, when the displacement is 2cm that is 0.02m, the potential energy is V
So, \[U=\dfrac{k{{x}^{2}}}{2}\]
\[V=\dfrac{k\times {{0.02}^{2}}}{2}\]---------(1)
Now when the displacement is 10 cm that is 0.1m,
\[U=\dfrac{k\times {{0.1}^{2}}}{2}\]---------(2)
Dividing eq (2) by eq (1) we get,
$
\dfrac{U}{V}=\dfrac{0.01}{0.0002} \\
\therefore U=25V \\
$

So the value of potential energy, in this case, comes out to be 25 V, and hence, the correct option is (D).

Note:
While calculating the potential energy of the spring both the spring constant and the displacement from the equilibrium position are to be taken in standard SI units and the energy is measured in Joules, J.