Question

Figure shows that 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 above fact, the minimum safe value for the radius of curvature at point $B$ is $(g=10m/s^2)$

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

Answer 1

The correct option is A $20m$

Given,

Height difference is $H=25-15=10m$

Kinetic energy = potential energy

$\frac{1}{2}m{v}^2=mgH$

$v^2=2gH.....\left(1\right)$

To have some positive normal reaction

Weight of car > Centripetal force

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

$\Rightarrow r=\frac{v^2}{g}=\frac{2gH}{g}=2\times 10=20m$