Question

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

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

Answer 1

The correct option is D $2cm$

For successfully completing the loop, Normal Reaction at highest point should be greater than 0.

Normal reaction at D:

$N_D=\frac{m{v}_D^2}{R}-mg$

$N_D>0$

$v_D>\sqrt{gR}$

Applying Energy conservation between point A nad D:

$mgh=mg\left(2R\right)+\frac{1}{2}m{v}_D^2$

putting least value of $v_D=\sqrt{gR}$

$mgh=mg\left(2R\right)+\frac{1}{2}mgR$

$h=\frac{5}{2}R=5cm$

$\therefore R=2cm$