The potential energy of a long spring when&nb | vedclass

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Question

$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,Potential\,energy\,of\,a\,\,{m{spring}}\
{m{ = }}\frac{1}{2} 	imes \,force{m{ constant}}\, 	imes {\

Vedclass · Accepted Answer

$16U$

Vedclass · Answer

$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,Potential\,energy\,of\,a\,\,{m{spring}}\
{m{ = }}\frac{1}{2} 	imes \,force{m{ constant}}\, 	imes {\left( {extension} ight)^2}\
	herefore \,Potential\,energy \propto \,{\left( {extension} ight)^2}.\
or,\,\frac{{{U_1}}}{{{U_2}}} = {\left( {\frac{{{x_1}}}{{{x_2}}}} ight)^2}\,\,\,\,or,\,\,\frac{{{U_1}}}{{{U_2}}} = {\left( {\frac{2}{8}} ight)^2}\
or,\,\frac{{{U_1}}}{{{U_2}}} = \frac{1}{{16}}\,\,or,\,{U_2} = 16{U_1} = 16U.\,\,\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{U_1} = U} ight)
\end{array}$

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

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