Question

An inclined plane ends into vertical loop of radius $R$. A particle is released from height $3R$. Can it loop the loop?

• A. yes
• B. no
• C. cannot say
• D. yes if fraction is present

Answer 1

The correct option is A yes

The minimum speed required at the bottom of the circle(r) to complete the circular motion is $\sqrt{5gR}$
For this speed, the minimum height required is
$0.5m{v}^2=mgh$
$\Rightarrow 0.5\left(5gR\right)=gh$
$\Rightarrow h=\frac{5}{2}R$
So, the minimum height from which the body has to released is 2.5R. We have a height of 3R, so the particle completes the vertical loop.
Option A.