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)

$2 \,cm$

Answer 2

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 $h=5\, cm$ $\therefore R=\frac{2 \times 5}{5}=2 \,cm$