Question

Figure $(8-W9)$ shows a loop-the-loop track of radius $R.$ A car (without engine) starts from a platform at a distance $h$ above the top of the loop and goes around the loop without falling off the track. Find the minimum value of $h$ for a successful looping. Neglect friction.

Answer 1

In case of min height:

Velocity at base of loop must be $\sqrt{5gR}$

$\begin{array}{c}\Rightarrow mg\left(R+h\right)=\frac{1}{2}m\left(5gR\right)\\ \Rightarrow R+h=2.5R\\ \Rightarrow h=1.5R\end{array}$.