Question

Charge +q is uniformly distributed throughout the volume of a fixed non-conducting solid sphere of radius R.Two identical small particles each of charge +q and mass m are projected towards each other along a narrow tunnel inside the sphere as shown in figure. (Neglect gravity) Choose the correct option(s).

• A. Linear momentum of system of particles is conserved.
• B. Linear momentum of system of particles is not conserved.
• C. Minimum value of u for which particles will just reach at the surface of the sphere is $\sqrt{\frac{5k{q}^2}{3mR}}$
• D. Minimum value of u for which particles will just reach at the surface of the sphere is $\sqrt{\frac{2k{q}^2}{mR}}$

Answer 1

Answer: (A), (C)

The correct options are
A Linear momentum of system of particles is conserved.
C Minimum value of u for which particles will just reach at the surface of the sphere is $\sqrt{\frac{5k{q}^2}{3mR}}$

Since the net external force on a system of particles is $0$, therefore linear momentum will be conserved.

Energy conservation (For minimum $u$ final kinetic energy $=0$)
$\frac{1}{2}m{u}^2+\frac{1}{2}m{u}^2+q\times \left[\frac{kq}{3R}\right]\times 2+\frac{k{q}^2}{6R}$

$=0+0+q\times \left[\frac{kq}{R}\right]\times 2+\frac{k{q}^2}{2R}$
$\Rightarrow u=\frac{5k{q}^2}{3mR}$