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Question

A particle is initially at rest, moves along in a circle of radius R=2 m with an angular acceleration α=π8 rad/sec2. The magnitude of average velocity of the particle over the time it moves by half of the circle is

A
4 m/s
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B
3 m/s
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C
2 m/s
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D
1 m/s
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Solution

The correct option is D 1 m/s
Given, radius of circle R=2 m, angular acceleration α=π8 rad/s2
Since, particle was initially at rest, ω0=0
Using the formula,
θ=ω0t+12αt2 where, θ is the angular displacement
θ=12αt2=πt216 ...(i)
Also, we have for half circle, θ=π ...(ii)
Using (i) & (ii) we have
π=πt216 t2=16 t=4 sec
Now, average velocity is given by
vavg=total displacementtotal time taken
vavg=2R4=44=1 m/s

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