First slide

Rolling motion

Question

A solid cylinder rolls up along a long inclined plane of inclination θ with an initial velocity v. How far does the cylinder go up the plane? Assume pure rolling.

Moderate

A

$\large \frac{{3{v^2}}}{{2g\sin \theta }}$
B

$\large \frac{{{v^2}}}{{4g\sin \theta }}$
C

$\large \frac{{3{v^2}}}{{g\sin \theta }}$
D

$\large \frac{{3{v^2}}}{{4g\sin \theta }}$

Solution

Initial total K.E = Final P.E
$\large \Rightarrow\frac 12mv^2\left ( 1+\frac {K^2}{R^2} \right )=mgh$
$\large \Rightarrow\frac 12mv^2\left ( 1+\frac 12 \right )=mgh$
$\large \Rightarrow h=\frac {3v^2}{4g}$
$\large \therefore s=\frac {h}{sin\theta}=\frac {3v^2}{4gsin\theta}$

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