A) \[\frac{3{{u}^{2}}}{4g}\]
B) \[\frac{5{{u}^{2}}}{2g}\]
C) \[\frac{7{{u}^{2}}}{10g}\]
D) \[\frac{{{u}^{2}}}{2g}\]
E) \[\frac{11{{u}^{2}}}{9g}\]
Correct Answer: C
Solution :
The rolling sphere has rotational as well as translational kinetic energy. \[\therefore \]Kinetic energy \[=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}I{{\omega }^{2}}\] \[=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}\left( \frac{2}{5}m{{r}^{2}} \right){{\omega }^{2}}\] \[=\frac{1}{2}m{{u}^{2}}+\frac{1}{5}m{{u}^{2}}=\frac{7}{10}m{{u}^{2}}\] \[(\because \,\,u=r\omega )\] From conservation of energy, Potential energy = kinetic energy ie, \[mgh=\frac{7}{10}m{{u}^{2}}\] or \[h=\frac{7{{u}^{2}}}{10g}\]
You need to login to perform this action.
You will be redirected in
3 sec
