A) \[{{t}^{2}}\]
B) \[{{t}^{{1}/{2}\;}}\]
C) \[{{t}^{3}}\]
D) \[{{t}^{{2}/{3}\;}}\]
Correct Answer: C
Solution :
\[P=Fv=mav=m\,\,v\,\,dv/dx=kx\] (given) where \[k\]is any constant. \[mvdv=kxdx\] on integration we have \[\frac{m{{v}^{2}}}{2}=\frac{k{{x}^{2}}}{2}\] \[\because p=mav=kx\] \[\therefore \]\[mv\frac{dv}{dt}=k\sqrt{\frac{m{{v}^{2}}}{k}}={{\left( \sqrt{km} \right)}_{v}}\] \[dv=\frac{\left( \sqrt{7km} \right)}{m}dt\] On integration we have \[v=\left( \sqrt{\frac{k}{m}} \right)\times t\] \[\frac{dx}{dt}=\sqrt{\frac{kxt}{m}}\] \[\frac{dx}{\sqrt{x}}=\sqrt{\frac{k}{m}}{{t}^{1/2}}dt\] \[2\sqrt{x}=\sqrt{\frac{k}{m}}\frac{2}{3}{{t}^{\frac{2}{3}}}\] \[x\]is proportional to \[{{t}^{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
