A bullet of mass m and chage Q is fired towards a solid uniformly charged sphere of radius R and total charge +q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistant forces of friction acting on bullet except electrostatic forces.)

Vikas TU
14149 Points
6 years ago
Dear Student,

Force of repulsion = kQq/r^2
Force of bullet (F) = ma
These two force are equal
• ma = kQq/r^2
• a = kQq/mr^2
• As bullet strike the sphere with speed u
• S = u^2/2a = u^2kQq/2mr^2
• 2R= u2mr2/2KQq
• 4KQq/mR = u2
• U =2√ KQq/mR
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Yash Chourasiya
askIITians Faculty 256 Points
4 years ago
Hello Student

Total Energy of the system should be Conserve.

Total Energy at point 1 (On the surface) = Total Energy at point 2 (at the centre of sphere)
(K.E. + P.E.)1 = (K.E. + P.E.)2
(1/2mu2+ kq2/R) = (0 + (3kq2)/2R)

For further solution please see the Attachment.

I hope this solution will help you.