• # question_answer 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 $h=5\,cm.$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) $2\,cm$

For successful completion of the loop the speed of the body at the lowest point must be at least$\sqrt{5gR}.$Conserving Mechanical energy between the position A and B, we get $mgh=\frac{1}{2}m{{(\sqrt{5gR})}^{2}}$ $\therefore$    $h=\frac{5}{2}R$ So, for successful completion of the loop, the value of h must be atleast equal to $\frac{5}{2}$R. Or, $h\ge \frac{5}{2}R\Rightarrow \frac{5R}{2}\le h$ $\therefore$$R\le \frac{2h}{5}=\frac{2\times 5}{5}=2\,cm$ So, the maximum value of R must be equal to 2 cm Hence, the correction option is [d].