Radial & Tangential Acceleration for Non Uniform Circular Motion
A particle of...
Question
A particle of mass 2kg is moving in a circular path of constant radius 1m such that its centripetal acceleration ac is varying with time t as ac=100t2. The power delivered to the particle by the force acting on it in 5sec is
A
400W
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B
1000W
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C
500W
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D
0W
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Solution
The correct option is B1000W Given, Mass of the particle (m)=2kg Radius of circular path (r)=1m Centripetal acceleration of particle (ac)=100t2 Time (t)=5sec Force acting on the particle is centripetal in nature (Fc). In circular motion, only tangential force provides power as FC⊥v and Ft||v
∴PC=→Fc.→v=0 and Pt=→Ft.→v≠0 Now, ac=100t2 ⇒v2r=100t2 ⇒ Speed (v)=10t By definition, tangential acceleration at=dvdt ∴at=10m/s2 i.e Tangential force (Ft)=mat=20N As discussed earlier, power is delivered to the particle only by the action of tangential force. ∴ Power (Pt)=→Ft.→v=Fvcosθ=20×10t×cos00=200t At t=5sec Pt=200×5=1000W Hence, option (b) is the correct answer.