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 be a) 625 J b) 250 J c) 500 J d) 125 J

Options

A. `525` Joule
B. `550` Joule
C. `600` Joule
D. `625` Joule

Answer

D

Explanation

A particle…………..
`F = (-dU)/(dx), F = (-d(2r^(3)))/(dr) = - 6r^(2)`
`F = (mv^(2))/(R ) = 6r^(2)`
(required centripetal force)
`mv^(2)=6r^(3)`
`KE = (1)/(2)mv^(2)=3r^(3)`
`PE = 2r^(3)`
Total energy `= 5r^(3)=5(5)^(3)=625` Joule