The potential energy of a long spring when stretched by $2 ext{ cm}$ is $U$. If the spring is stretched by $

Question

The potential energy of a long spring when stretched by $2 	ext{ cm}$ is $U$. If the spring is stretched by $8 	ext{ cm}$, potential energy stored in it will be

Accepted Answer

Potential energy of a spring $U = \frac{1}{2}kx^2$. Thus $U \propto x^2$. If $x$ increases from $2 	ext{ cm}$ to $8 	ext{ cm}$ (a factor of 4), the energy increases by a factor of $4^2 = 16$. So, new energy is $16U$.

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