Question

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

• A. 16U
• B. 2U
• C. 4U
• D. 8U

Answer 1

Answer: (A)

16U

Answer 2

The correct option is (A): 16U

The potential energy of a spring = \frac{1}{2}x$$\timesforce constant$\times$(extension)2

potential energy $\propto$ (extension)2

or, $\frac{U_1}{U_2}=(\frac{x_1}{x_2})^2=(\frac{2}{8})^2=\frac{1}{16}$

or, $U_2=16\,U_1=16U$($\because U_1=U$)