Question

A spring with spring constant $k$ when stretched through $1cm$, the potential energy is $U$. If it is stretched by $4cm$. The potential energy will be

• A. $2U$
  
• B. $4U$
  
• C. $8U$
  
• D. $16U$
  

Answer 1

The correct option is D $16U$

$\frac{P{E}_1}{P{E}_2}=\frac{x_1^2}{x_2^2}=\frac{1^2}{4^2}=\frac{1}{16}$

$\Rightarrow P{E}_2=16\times P{E}_1=16U$

Hence correct answer is option $D$