2003 AIPMT Work, Energy and PowerPotential Energy of a Spring Easy Question 6 of 7 in Potential Energy of a Spring

When a long spring is stretched by 2 cm, its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be :

A $\dfrac{U}{5}$
B 5U
C 10U
D 25U

The answer is D.

Solution

Potential energy stored in a stretched spring: $U = \dfrac{1}{2}kx^2$, so $U \propto x^2$.
$U = \dfrac{1}{2}k(2)^2$ and $U' = \dfrac{1}{2}k(10)^2$
$\dfrac{U'}{U} = \dfrac{10^2}{2^2} = 25$
$U' = 25U$

Concept Spring potential energy proportional to x squared

Potential Energy of a Spring in past papers

7 questions from this chapter have appeared across 7 exam years.