b
પ્રારંભ માં \(\,{\text{k}}\ell \,\, = \,\,{\text{Mg}}\,\, \Rightarrow \,\,{\text{k}}\,\, = \,\,\frac{{{\text{5}}\,\, \times \,\,{\text{10}}}}{{{\text{0}}{\text{.1}}}}\,\, = \,\,500\,\,N/m\)

ધારો કે તે ઊંચાઈ સુધી જતો હોય ત્યારે સ્પ્રિંગમાં થતું સંકોચન  \(\,{\text{(h}}\,\,{\text{ - }}\,\,\ell {\text{)}}\)

ઉર્જા સરક્ષણ ના નિયમ પરથી, \(\,\,\frac{{\text{1}}}{{\text{2}}}\,\,M{v^2}\, + \,\,\frac{1}{2}\,K{\ell ^2}\, = \,\,Mgh\,\, + \,\,\frac{1}{2}\,\,K\,{(h\,\, - \,\,\ell )^2}\)

\( \Rightarrow \,\,\,M{v^2}\, + \,\,K\,[{\ell ^2}\, - \,\,{(h\,\, - \,\,\ell )^2}]\,\, = \,\,2Mgh\,\, \Rightarrow \,\,M{v^2}\, + \,\,K\,[h(2\ell \,\, - \,\,h)]\,\, = \,\,2mgh\)

\( \Rightarrow \,\,20\,\, + \,\,500\,[h(0.2\, - \,\,h)]\,\, = \,\,100\,h\,\, \Rightarrow \,\,1\,\, + \,\,25\,\,(0.2h\, - \,\,{h^2})\,\, = \,\,5h\)

\( \Rightarrow \,\,\,1\,\, + \,\,5h\,\, - \,25{h^2}\, = \,\,5h\,\, \Rightarrow \,\,{h^2}\, = \,\,\frac{1}{{25}}\,\, \Rightarrow \,\,h\,\, = \,\,\frac{1}{5}\,\, = \,\,0.2\,m\)