Electrostatics> A bullet of mass m and chage Q is fired t...

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.)

kunal gadhavi , 8 Years ago

Grade 11

2 Answers

Vikas TU

Last Activity: 7 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. 4^th year
Thapar University)

Yash Chourasiya

Last Activity: 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.