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

• A. $v^{2} / g$
• B. $v^{2} / 2 g$
• C. $v^{2} / 3 g$
• D. $3 v^{2} / 4 g$

Answer 1

Answer: (D)

$\frac{1}{2} M v^{2}+\frac{1}{2} I \omega^{2}=M g h$
$\Rightarrow \frac{1}{2} M v^{2}+\frac{1}{2} \frac{1}{2} M R^{2}\left(\frac{v}{R}\right)^{2}=M g h \Rightarrow h=\frac{3 v^{2}}{4 g}$