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A charge +Q is uniformly distributed in ...

A charge `+Q` is uniformly distributed in a spherical volume of radius R. A particle of charge `+q` and mass m projected with velocity `v_0` the surface of the sherical volume to its centre inside a smooth tunnel dug across the sphere. The minimum value of `v_0` such tht it just reaches the centre (assume that thee is no resistance on the particle except electrostatic force) of he sphericle volume is

A

`sqrt((Qq)/(2piepsilon_0mR))`

B

`sqrt((Qq)/(piepsilon_0mR))`

C

`sqrt((2Qq)/(piepsilon_0mR))`

D

`sqrt((Qq)/(4piepsilon_0mR))`

Text Solution

Verified by Experts

The correct Answer is:
D
`U_i+K_i=U_f+k_f`
`or qV_i+1/2mv_(min)^2=qV_f+0`
`=or q(1/(4piepsilon_0))(Q/R)+1/2mv_(min)^2+q[3/2xxQ/(4piepsilon_0R)]`
from here we can find `v_(min)`
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