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Question

A particle of mass 2 kg is moving in a circular path of constant radius 1 m 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 5 sec is

A
400 W
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B
1000 W
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C
500 W
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D
0 W
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Solution

The correct option is B 1000 W
Given,
Mass of the particle (m)=2 kg
Radius of circular path (r)=1 m
Centripetal acceleration of particle (ac)=100 t2
Time (t)=5 sec
Force acting on the particle is centripetal in nature (Fc).
In circular motion, only tangential force provides power as FCv and Ft||v


PC=Fc.v=0 and Pt=Ft.v0
Now, ac=100t2
v2r=100t2
Speed (v)=10t
By definition, tangential acceleration at=dvdt
at=10 m/s2
i.e Tangential force (Ft)=mat=20 N
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=5 sec
Pt=200×5=1000 W
Hence, option (b) is the correct answer.

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