A particle of mass m is moving in a circular path of radius r under the influence of centripetal force F - C - r 2 - The total energy of the particle isA- -C-2 rB- -2 rC- C - 2 rD- ZeT O

F centripetal F=mv^2/r=C/r^2; U= ∫ _αF dr=C∫ r^ 2dr= C/r; ∴ E_1=E_k+U=C/2r C/r= C/2r ...

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Standard XII

Physics

Law of Conservation of Mechanical Energy

A particle of...

Question

A particle of mass m is moving in a circular path of radius r under the influence of centripetal force $F = \frac{- C}{r^{2}}$ . The total energy of the particle is

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Solution

The correct option is A
F centripetal $F = \frac{m v^{2}}{r} = \frac{C}{r^{2}}; U = - \int_{α} F d r = C \int r^{- 2} d r = \frac{- C}{r}; ∴ E_{1} = E_{k} + U = \frac{C}{2 r} - \frac{C}{r} = - \frac{C}{2 r}$

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