Question

A uniform chain is stretched by 2 cm , its potential energy is U . if the spring is stretched by 10 cm ,the potential energy stored in it will be ?​

Answer 1

Aɴꜱᴡᴇʀ

$\bf{\green{U'=25U}}$

_________________

Gɪᴠᴇɴ

Spring stores U potential energy when stretched by 2cm

_________________

ᴛᴏ ꜰɪɴᴅ

Potential energy stored in spring when stretched by 10cm

_________________

Sᴛᴇᴘꜱ

Formula of stored potential energy in spring is

$\dashrightarrow{ \pink{\tt\:U=\dfrac{1}{2}kx^2}}$

U denotes potential energy

k denotes spring constant

x denotes elongation

As per formula of energy stored in spring, It is clear that...

$\begin{lgathered}\sf\bigstar\red\:U\propto x^2\\ \\ \leadsto\sf\:\dfrac{U}{U'}=\dfrac{{x_1}^2}{{x_2}^2}\\ \\ \leadsto\sf\:\dfrac{U}{U'}=\dfrac{4}{100}\\ \\ \leadsto\sf\:\dfrac{U}{U'}=\dfrac{1}{25}\\ \\ \dashrightarrow\bf{\red{U'=25U}}\end{lgathered}$

_________________

$\huge{\mathfrak{\purple{hope\; it \;helps}}}$