A particle is moving in a circle of radius ‘r’ under the action of a force $F = α r^{2}$ , which is directed towards centre of the circle. Total mechanical energy of the particle is (take P.E. = 0 at r = 0)

Question

Infinity Learn · Accepted Answer

Centripetal force   F $$=$$  α$$r2$$  ∴    $$mv2r$$   $$=$$    α$$r2$$   ⇒   $$mv2$$   $$=$$    α⋅$$r3$$   ∴   K.E.   $$=$$    $$12$$ $$mv2$$    $$=$$   $$12$$  α$$r3$$     ∴   P.E.   $$=$$   U $$=$$∫ F.dr  $$PE$$ $$=$$  ∫ α$$r2$$⋅ dr  $$PE$$ $$=$$    α$$r33$$  ∴      Total energy $$=P$$.E.  $$+K$$.E substitute above obtained values,  $$TE$$  $$=$$   α$$r33$$ $$+$$  $$12$$  α$$r3$$ $$TE$$$$=$$ $$56$$  α$$r3$$

A particle is moving in a circle of radius ‘r’ under the action of a force $F = α r^{2}$ , which is directed towards centre of the circle. Total mechanical energy of the particle is (take P.E. = 0 at r = 0)

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A particle is moving in a circle of radius ‘r’ under the action of a forceF = αr2, which is directed towards centre of the circle. Total mechanical energy of the particle is (take P.E. = 0 at r = 0)

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A particle is moving in a circle of radius ‘r’ under the action of a force $F = α r^{2}$ , which is directed towards centre of the circle. Total mechanical energy of the particle is (take P.E. = 0 at r = 0)