Question

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

• A. $5\text{cm}$
• B. $\frac{15}{4}\text{cm}$
• C. $\frac{10}{3}\text{cm}$
• D. $2\text{cm}$

Answer 1

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

Velocity of the block when it reaches bottom most point (B) of the track is $v=\sqrt{2gh}$
Velocity of the block at B for looping the loop is $v=\sqrt{5gR}$

$\therefore \sqrt{2gh}=\sqrt{5gR}$
$\Rightarrow h=\frac{5}{2}R=5\text{cm}$
$\therefore R=2\text{cm}$