Question
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force given by `( -k/r^2)`, where k is a constant, them
Answer: Option A
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Centripetal force = `(mv^2)/(r) = k/r^2`
`:.` `mv^2 = k/r`
`:.` Kinetic energy is `1/2 mv^2 = (k)/(2r)`
`:.` `F = - (k)/(2r), F = (du)/(dr)`
At infinity , potential energy is zero
`:.` `int_u^0 du = - int _r^oo Fdr`
`:.` `u = - k [ - 1/r]_r^oo = - k/r`
`:.` Total energy = `K.E. + u`
= `(k)/(2r) - k/r = - (k)/(2r)`
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