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Question

A wheel has six equally spaced thin spokes of length 20 cm. It is rotating about an axis xx' which is perpendicular to its plane and passing through its center with 5 rev/sec. What should be the minimum velocity of an arrow of length 30 cm to pass the wheel without hitting any spoke. (Arrow is projected parallel to the axis).


A
9 m/s
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B
4 m/s
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C
5 m/s
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D
4.5 m/s
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Solution

The correct option is A 9 m/s
Angle between successive spokes is,
Δθ=2π6=π3
Angular speed of wheel ω=5 rps=(5×2π) rad/s
ω=10 π rad/s
Time taken by one spoke to pass is,
t=Δθω=(π3)10 π
t=130s
During this time interval, the arrow must pass through.
x=v×t
x=length of arrow = 30 cm = 0.3 m
v=0.30(1/30)=9 m/s
So, minimum velocity of arrow will be 9 m/s
Thus, option (a) is the correct answer.

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