Question

A wheel of radius $0.2$m rolls without slip ping with a speed $10$m/s on a horizontal road. When it is at point A on the road, a small limp of mud separates from the wheel at its highest point B and drops at point C on the ground .The distance AC is

• A. $4.45$m
• B. $7.45$m
• C. $5.45$m
• D. $9.45$m

Answer 1

The correct option is C $5.45$m

Radius ofthe wheel roll$=2n=r$

Speed $=10m/s$ on horizontal

road$=V$

The distance $AC=?$

AC$=range=\left(2v\right)\times t_{flight}=\left(2v\right)\sqrt{\frac{2\left(2r\right)}{g}}$

AC$=4v\sqrt{\frac{r}{g}}=4v\times \sqrt{\frac{r}{g}}=4\times 10\sqrt{\frac{0.2}{10}}=4\times 10\sqrt{\frac{2}{10\times 10}}=40\sqrt{\frac{1}{50}}=5.65m$