A) \[{{x}^{2}}\]
B) \[{{e}^{x}}\]
C) \[x\]
D) \[{{\log }_{e}}x\]
Correct Answer: A
Solution :
From given information\[a=-kx\], where \[a\] is acceleration, \[x\] is displacement and \[k\] is a proportionality constant. \[\frac{v\,\,dv}{dx}=-k\,\,x\] \[\Rightarrow \] \[v\,\,dv=-k\,\,x\,\,dx\] Let for any displacement from \[0\] to \[x\], the velocity changes from\[{{v}_{0}}\]to\[v\] \[\Rightarrow \] \[\int_{{{v}_{0}}}^{v}{vdv=}-\int_{0}^{x}{k\,\,x\,\,}dx\] \[\Rightarrow \] \[\frac{{{v}^{2}}-v_{0}^{2}}{2}=-\frac{k\,\,{{x}^{2}}}{2}\] \[\Rightarrow \] \[m\left( \frac{{{v}^{2}}-v_{0}^{2}}{2} \right)=-\frac{mk\,\,{{x}^{2}}}{2}\] \[\Rightarrow \] \[\Delta K\propto {{x}^{2}}\] \[[\Delta K\]is loss in\[KE]\]
You need to login to perform this action.
You will be redirected in
3 sec
