Question

A small disc is set rolling with a speed $v$ on the horizontal part of the track from the lower part of tack to upper part as shown in figure. To what height will it climb up the curved part?

Answer 1

A disc is set rolling with a velocity $V$ form right to left to left it has attained

For pure rolling We know that, $V=Rw$ $\Rightarrow$ $w=\frac{V}{R}$

Now we apply energy conservation equation,

Therefore $\left(1/2\right)m{V}^2+\left(1/2\right)l{\omega }^2=mgh$

$\Rightarrow \left(1/2\right)m{V}^2+\left(1/2\right)\times \left(1/2\right)m{R}^2{\omega }^2=mgh$

$\Rightarrow \left(1/2\right)V^2+1/4V^2=gh\Rightarrow \left(3/4\right)V^2=gh$

$\Rightarrow h=\frac{3}{4}\times \frac{V^2}{g}$