Question

A wheel of radius $r$ rolls without slipping on the ground, with speed $v$. When it is at a point $P$, a piece of mud flies off tangentially from its highest point, lands on the ground at point $Q$. The distance $PQ$ is:

• A. $2v\sqrt{\left(r/g\right)}$
• B. $2\sqrt{2}v\sqrt{\left(r/g\right)}$
• C. $4v\sqrt{\left(r/g\right)}$
• D. $v\sqrt{\left(r/g\right)}$

Answer 1

The correct option is C $4v\sqrt{\left(r/g\right)}$

$AC=Range=Velocityofprojection\times timeofflight$

$Range=\left(2v\right)\times t_{flight}$

$=\left(2v\right)\times \sqrt{\frac{2h}{g}}$

$=\left(2v\right)\times \sqrt{\frac{2\left(2r\right)}{g}}$ where, $h=2r$

$=\left(4v\right)\sqrt{\frac{r}{g}}$