Question

- a ball of mass m and having charge q is tied at one end of a thread of length l.The other end of the thread is fixed and a similar charge q is placed on it. The ball can move in the circular orbit of radius l in vertical plane.Initially the ball is at bottom and is at rest. Find the minimum horizontal velocity given to the ball so as it can complete one full circle. From

Answer 1

Answer:

Explanation:

Let u be the velocity which is given to ball at start

To complete the circular motion the limiting condition is T greater or equal than 0 at top most point

Let velocity at the top most point be v, therefore tension can be written as

T plus m g minus fraction numerator K q squared over denominator l squared end fraction equals fraction numerator m v squared over denominator l end fraction

T greater or equal than 0

fraction numerator m v squared over denominator l end fraction minus m g plus fraction numerator K q squared over denominator l squared end fraction greater or equal than 0

v greater or equal than square root of g l minus fraction numerator K q squared over denominator m l end fraction end root

B y space u sin g space e n e r g y space c o n s e r v a t i o n

1 half m u squared plus fraction numerator K q squared over denominator l end fraction plus 0 equals 1 half m v squared plus fraction numerator K q squared over denominator l end fraction plus 2 m g l

1 half m u squared equals 1 half m open parentheses g l minus fraction numerator K q squared over denominator m l end fraction close parentheses plus 2 m g l

u equals square root of 5 g l minus fraction numerator K q squared over denominator m l end fraction end root