Question

As shown in figure, a loop-the-loop track of radius $r=10\text{m}$. A box starts sliding from a platform at a distance $h$ above the top of the loop and goes around the loop without falling off the track. Find the minimum value of $h$ for successful looping. (Assume friction is negligible at all surfaces).

• A. $5\text{m}$
• B. $10\text{m}$
• C. $\frac{5}{2}\text{m}$
• D. $20\text{m}$

Answer 1

The correct option is A $5\text{m}$

To complete the loop the box must have its speed at least $\sqrt{5gr}$ at bottom of the loop, otherwise it will loose contact.
Hence from work energy theorem from top point to bottom point of the loop.
$mg(h+2r)+0=\frac{1}{2}m{v}^2$
(Here $v=\sqrt{5gr}$)
$mg(h+2r)=\frac{1}{2}m\left(5gr\right)$
$2h+4r=5r$
$h=\frac{r}{2}=\frac{10}{2}$
$h=5\text{m}$