Question

A wheel of radius $30cm$ has $8$ spokes in it. It is mounted on a fixed axle and spins at $5rev/s$. If an arrow of length $24cm$ is to be shot parallel to the axis of the wheel without hitting rim or the spokes of the wheel. What minimum speed the arrow must have? (Ignore the effect of gravity)

• A. $9.6m/s$
• B. $4.8m/s$
• C. $2.4m/s$
• D. $19.2m/s$

Answer 1

The correct option is A $9.6m/s$


Given: $\omega =5rad/s$, Radius of the wheel is $30cm$
$t\to$ Maximum time required by the arrow to pass the wheel
Time $t=\frac{\frac{1}{8}}{5}$
As we know that, speed $=$ distance/time $=$$\frac{24\times {10}^2}{\frac{1}{8}}=\frac{48}{5}=9.6$
$\therefore$ Speed of the arrow must be $9.6m/s$

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