Question

The potential energy of a long spring when stretched by $2cm$ is $U$ . If the spring is stretched by $8cm$ the potential energy stored in it is

• A. 4 U
• B. 8 U
• C. 16 U
• D. U/4

Answer 1

Answer: (C)

Let extension produced in a spring be $x$ initially.
In stretched condition spring will have potential energy
$U=\frac{1}{2}k{x}^2$
Where $k$ is spring constant or force constant,
$\therefore \frac{U_1}{U_2}=\frac{x_1^2}{x_2^2}$ ...(i)
Given, $U_1=U,x_1=2cm,x_2=8cm$
Putting these values in Eq. (i), we have
$\frac{U}{U_2}=\frac{(2{)}^2}{(8{)}^2}=\frac{4}{64}=\frac{1}{16}$
$\therefore U_2=16U$