Question

A solid disk is rolling without slipping on a level surface at a constant speed of $2.00m/s$. How far can it roll up a ${30}^{\circ }$ ramp before it stops? (Take $g=9.8m/s^2)$

Answer 1

$mgh=K_R+K_r=\frac{3}{4}m{v}^2$
Here $h=s\sin \theta$
$\therefore gs\sin \theta =\frac{3}{4}{v}^2$ or
$s=\frac{3v^2}{4g\sin \theta }$
$=\frac{3\times (2.0{)}^2}{4\times 9.8\times \frac{1}{2}}$
$=0.612m$