Question

A frictionless track $\text{ABCDE}$ ends in a circular loop of radius $R$. A body slides down the track from point $\text{A}$ which is at a height $h=5\text{cm}$. Maximum value of $R$ for a body to complete the loop successfully is

• A. $2\text{cm}$
• B. $\frac{10}{3}\text{cm}$
  
• C. $\frac{15}{4}\text{cm}$
• D. $\frac{18}{3}\text{cm}$

Answer 1

The correct option is A $2\text{cm}$

In a vertical circular motion we know that the condition of looping the loop is $u\ge \sqrt{5gR}$

For maximum radius possible we have,

$u=\sqrt{5gR}$

Applying conservation of energy between points $\text{A}$ and $\text{B}$ we get,

$mgh=\frac{1}{2}m{v}^2$

$v=\sqrt{2gh}$

$v=\sqrt{2gh}=\sqrt{2g\left(5\right)}=\sqrt{10g}$

But we know that,

$\sqrt{10g}\ge \sqrt{5gR}$

$\Rightarrow R_{max}=2\text{cm}$

Why this Question ? Note: Condition for looping the loop is $u\ge \sqrt{5gR}$ Where $u$ is the speed of particle at the bottom of the loop.