Question

Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the given fact, the minimum safe value for the radius of curvature at point B is $(g=10m/s^2)$:

• A. $20$ m
• B. $10$ m
• C. $40$ m
• D. $25$ m

Answer 1

The correct option is A $20$ m

Speed at point $B=\sqrt{2gh}$

$=\sqrt{2\times 10\times (25-5)}=10\sqrt{2}\frac{m}{s}$

For minimum radius of curvature $r$,

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

$r=\frac{200}{10}=20$