1.

A body of mass `2 kg` is moving under the influence of a central force whose potential energy is given by `U = 2r^(3) J`. If the body is moving in a circular orbit of `5 m`, its energy will beA. `625 J`B. `250 J`C. `500 J`D. `125 J`

Answer» Correct Answer - A
`F = - (dU)/(dr) = - 6r^(2)`
Now `(m nu^(2))/(r) =6r^(2)`
`:. (1)/(2) m nu^(2) = 3r^(3)`
`E = K + U = 3r^(3) + 2r^(3) = 5r^(3)`
At `r = 5m, E = 625 J`


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