Question

A $250g$ thin hoop with a radius of $25.0$ centimeters is initially rotating at $15.0rev/s$. It takes $30.0$ revolutions for the hoop to roll to a stop.
If the hoop rolls without slipping, over what linear displacement does the hoop roll?

• A. $7.5m$
• B. $15.0m$
• C. $28.0m$
• D. $47.1m$
• E. $65.0m$

Answer 1

Answer: (D)

$47.1m$

Given : Radius of hoop $r=25$ cm $=0.25$ m

Number of revolution $N=30.0$

Thus angular displacement covered $\theta =2\pi \times 30=188.4$ $rad/s$

$\therefore$ Linear displacement traveled $S=r\theta =0.25\times 188.4=47.1$ $m$