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Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec it rotates through an angle θ1, in the next 2 sec it rotates through an additional angle θ2. The ratio of θ2θ1 is

A
1
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B
2
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C
3
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D
5
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Solution

The correct option is C 3
Let the uniform angular acceleration be α, the initial angular velocity ω0=0

We know that, the angular displacement for first two sec,
θ1=ω0t+12αt2, t=2 s
θ1=2α

let the angular velocity changes from ω0 to ω for the first 2 s, by the equation of motion under constant angular acceleration
ω=ω0+αtω=0+2α=2α

Now for the angular displacement for next time interval of 2 s
θ2=ωt+12αt2, t=2 s
θ2=4α+2α=6α

Hence the ratio,

θ2θ1=6α2α=3

(OR)

Let the uniform angular acceleration be α, the initial angular velocity ω0=0

The angular displacement for first two sec,
θ1=ω0t+12αt2, t=2 s
θ1=2α
The angular displacement for first four sec
θ1+θ2=ω0t+12αt2 , t=4
θ1+θ2=8α
θ2=6α
Hence the ratio,

θ2θ1=6α2α=3

Option C is the correct answer.

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