Question

A long string is stretched by 2cm and potential energy is v. If the string is stretched by 10 cm its potential energy is

Answer 1

potential energy in a string(spring) can be given by-

$v = \frac{1}{2} k \: {x}^{2} \\ v = \frac{1}{2} k {(2)}^{2} \\ v = 2k$
Let potential energy for 10cm stretch is v'
so,
$v' = \frac{1}{2} k \: {y}^{2} \\ v' = \frac{1}{2} k {(10)}^{2} \\ v' = 50k \\ v' = 25(2k) \\ v' = 25v$

The potential energy will be 25 times of initial stretch.