First slide

Rolling motion

Question

A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as shown in figure. The maximum height upto which it can reach is

Moderate

A

$\frac{v^{2}}{g}$
B

$\frac{v^{2}}{2 g}$
C

$\frac{v^{2}}{3 g}$
D

$\frac{3 v^{2}}{4 g}$

Solution

$\frac{1}{2} {Mv}^{2} + \frac{1}{2} {Iω}^{2} = Mgh$
$\Rightarrow \frac{1}{2} {Mv}^{2} + \frac{1}{2} \frac{1}{2} {MR}^{2} {(\frac{v}{R})}^{2} = Mgh \Rightarrow Mgh \Rightarrow h = \frac{3 v^{2}}{4 g}$

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