Question

A frictionless track $A B C D E$ ends in a circular loop of radius $R. A$ body slides down the track from point $A$ which is at a height $h = 5 \,cm$ . Maximum value of $R$ for the body to successfully complete the loop is

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

Answer 1

Answer: (D)

Potential energy of the body at point $A$
$=$ kinetic energy of the body at point $B$
$m g h=\frac{1}{2} m v^{2}$
$g h=\frac{v^{2}}{2}$
Velocity at lowest point in a vertical circle
$v=\sqrt{5 R g}$
$g h=\frac{5 R g}{2}$
$R=\frac{2 h}{5}$
But $h=5\, cm$
$\therefore R=\frac{2 \times 5}{5}=2 \,cm$