Question

Energy stored in the stretched spring is U, it is cut in two equal parts. If one part is stretched to
the same extension, then energy stored in this
spring is
(1) U
(2) 2 U
(3)U/2
(4) 4U​

Answer 1

Given:

Energy stored in the stretched spring is U, it is cut in two equal parts. One part is stretched to the same extension.

To find:

Energy stored in spring

Calculation:

Let initial spring constant be k and initial length be l ;

$\therefore \: k \times l = (k2) \times \dfrac{l}{2}$

$= > (k2) = 2k$

Now , initial energy is U ;

$U = \dfrac{1}{2} k {x}^{2} \: \: \: ......(1)$

Let energy in new spring be U_(2)

$U_{2} = \dfrac{1}{2} (k2) {( x)}^{2}$

$= > U_{2} = \dfrac{1}{2} \times 2k \times {(x)}^{2}$

$= > U_{2} = k {x}^{2}$

$= > U_{2} = 2\times \bigg( \dfrac{k {x}^{2} }{2} \bigg)$

$= > U_{2} = 2 \times \bigg( U\bigg)$

So, final answer:

$\boxed{ \sf{U_{2} = 2U}}$