Question

a spring when stretched by 2mm its potential energy becomes 4j if it is stretched by 10mm its potential energy is equal to

Answer 1

Let extension produced in a spring be x initially in stretched condition spring will have potential energy

$U=\frac{1}{2} kx^{2}$

Here, k is spring constant.

Thus, we can write,   $\frac{U_{1} }{U_{2} } =\frac{x_{1}^2  }{x_{2} ^2}$

Given  $U_{1} =4 J$ , $x_{1}=2 mm$ and $x_{2} = 10 mm$

Putting these values in above relation we get,

$\frac{4}{U_{2} } = \frac{(2)^{2} }{(10)^{2} }$

OR

$U_{2} =100 J$