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A body of mass 2 kg is moving under the ...

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

`525` Joule

B

`550` Joule

C

`600` Joule

D

`625` Joule

Text Solution

Verified by Experts

The correct Answer is:
D
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
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