GravitationHard
Question
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is :
(Take $k = \frac{1}{4\pi\epsilon_{0}}$ and assume $kQ^{2} > Gm^{2}$ where G is the Gravitational constant)
Options
A.$\sqrt{\frac{kQ^{2}}{4mR}\left( 1 - \frac{Gm^{2}}{kQ^{2}} \right)}$
B.$\sqrt{\frac{kQ^{2}}{4mR}\left( 1 + \frac{Gm^{2}}{kQ^{2}} \right)}$
C.$\sqrt{\frac{kQ^{2}}{2mR}\left( 1 - \frac{Gm^{2}}{kQ^{2}} \right)}$
D.$\sqrt{\frac{kQ^{2}}{2mR}\left( 1 - \frac{Gm^{2}}{2kQ^{2}} \right)}$
Solution
Using energy conservation
(2) $\left( \frac{1}{2}mu^{2} \right) - \frac{Gm^{2}}{4r} + \frac{KQ^{2}}{4r} = - \frac{Gm^{2}}{2r} + \frac{KQ^{2}}{2r}$
$$u = \sqrt{\frac{1}{4mr}\left( KQ^{2} - Gm^{2} \right)}$$
Create a free account to view solution
View Solution FreeMore Gravitation Questions
A planet is revolving around the sun is an elliptical orbit as shown in figure. Select correct alternative(s)...A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the Sun is rmin. The farthest dis...Suppose, the acceleration due to gravity at the Earth′s is 10 ms-2 and at the surface of Mars it is 4.0 ms-2. A 60...If the gravitational force were to vary inversely-as mth power of the distance, then the time period of a planet in circ...The height at which the acceleration due to gravity becomes (where g = the acceleration due to gravity on the surface of...