A particle of mass m is moving in a horizontal circle of radius r under centripetal force equal to −Kr2, where K is a constant. The total energy of the particle is:
−K2r
−K2r2
K2r
−Kr2
A
−K2r2
B
−Kr2
C
K2r
D
−K2r
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Solution
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Centripetal force =mv2r=kr2 ...(given)
Kinetic Energy =12mv2=12kr
Potential Energy =−∫r∞Fdr
the lower limit has been taken as∞ because potential energy is zero at infinty
=−∫r∞kr2dr
=−k∫r∞r−2dr
=−k∣∣r−1−1∣∣r∞
=−kr
Total energy =k2r−kr=−k2r
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A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to −Kr2 , where K is a constant. The total energy of the particle is