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Two concentric rings placed in a gravity...

Two concentric rings placed in a gravity free region in yz-plane one of radius R carries `a + Q` and second of radius `4R` and charge `–8Q` distributed uniformly over it. Find the velocity with which a point charge of mass m and charge `+q` should be projected from a a distance `3R` from the centre of rings on its axis so that it will reach to the centre of the rings.

Text Solution

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The correct Answer is:
A, B, C
From energy conservation principle
`K_i+U_i=K_f+U_f`
`or 1/2mv^2+(+q)V_i=0(+q)V_f`
or `v=sqrt((2q)/m(-V_i+V_f))`
`sqrt((2a)/m[(-Q)/(sqrt(10)R)+(8Q)/(5R)+Q/R-(8Q)/(4R)] 1/(4piepsilon_0))`
`=sqrt((Qq)/(2piepsilon_0mR) ((3sqrt(10)-5)/(5sqrt10)))`
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