Question

A wheel has eight equally spaced, very thin spokes of length $30cm$. It is rotating about an axis OO' which is perpendicular to its plane and passing through the centre, with $2.5rps$. We want to pass a $20cm$ long arrow parallel to the axis and without hitting any spoke. What should be the minimum horizontal velocity of the arrow?

• A. $3m/s$
• B. $4m/s$
• C. $5m/s$
• D. $6m/s$

Answer 1

The correct option is B $4m/s$

Time to pass one spoke $t=\frac{\theta }{\omega }=\frac{\pi /4}{\left(2.5\right)\left(2\pi \right)}=\frac{1}{20}s$
For arrow $V=\frac{S}{t}=\frac{0.2m}{1/20s}=4m/s$