Question

A toy car starts from rest at position 1 shown in figure and moves without friction along the loop 12324:-

• A. the smallest height h at which the car can negotiate without falling off the track is r/2
• B. if car just negotiates the loop, the speed of car at position 4 is $\sqrt{5r}$
• C. if car just negotiates the loop, the speed of car at position 2 is 6 mg
• D. if car just negotiates the loop, the speed of car at position 3 is ma

Answer 1

The correct option is A the smallest height h at which the car can negotiate without falling off the track is r/2

When h has its critical value, the car will just lose contact with the track at (3) . Then at 3, normal force due to loop vanishes,

$mg=\frac{m{v}_3^2}{r}$

$v_3^2=gr$

By conservation of Energy

$mgh=\frac{1}{2}m{v}_3^2$

$h=\frac{v_3^2}{2g}$

$=\frac{gr}{2g}=\frac{r}{2}$