A) \[v'=2{{v}_{e}}\]
B) \[v'=\sqrt{7}{{v}_{e}}\]
C) \[\sqrt{2}{{v}_{e}}=v'\]
D) \[v'={{v}_{e}}\]
Correct Answer: B
Solution :
Idea This question is based on conservation of mechanical energy. Here, one should observe that the summation of gravitational PE and KE will remain constant. We can apply mechanical energy conservation \[{{(TME)}_{i}}={{(TME)}_{f}}\] \[-\frac{G{{M}_{e}}m}{{{R}_{e}}}+\frac{1}{2}m{{\left( 3\times \sqrt{\frac{G{{M}_{e}}}{{{R}_{e}}}} \right)}^{1/2}}={{(PE)}_{\infty }}+\frac{1}{2}m{{v}^{'2}}\]\[-\frac{G{{M}_{e}}m}{{{R}_{e}}}+\frac{9}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}=\frac{1}{2}mv{{'}^{2}}\] \[\frac{7}{2}\frac{G{{M}_{e}}}{{{R}_{e}}}=\frac{1}{2}v{{'}^{2}}\] \[v'=\sqrt{\frac{7G{{M}_{e}}}{{{R}_{e}}}}=\sqrt{7}{{v}_{e}}\] TEST Edge Similar questions where an object is thrown upwards from the earth's surface or where two objects are attracted towards each other could be asked. These questions could be solved easily by just applying the conservation of mechanical energy.
You need to login to perform this action.
You will be redirected in
3 sec
