Question

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

• A. $U/5$
• B. $5U$
• C. $10U$
• D. $25U$

Answer 1

The correct option is D $25U$

The potential energy stored in the spring is given by:

$U=\frac{1}{2}K{x}^2$

For stretch of 2cm, the energy is U. So,

$U=\frac{1}{2}K(2{)}^2$

Therefore, the energy stored in the stretch of $10cm$ will be:

$U^{\prime }=\frac{1}{2}K(10{)}^2$

$U^{\prime }=25\times \frac{1}{2}K\times 4⟹25U$