Question

in a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane the minimum speed at the highest point of tranquility

Answer 1

for the stability at the highest point without losing the contact the minimum speed required will be such speed so that it will have normal force just equal to zero at that point

Now as per force equation we can write

$F_{net} = ma$

at the top most point net force will be

$F_{net} = mg - F_n$

here for the minimum speed we can say that normal force is just ZERO

$F_{net} = mg$

now we can say

$mg = ma_c$

here we have

$a_c = \frac{v^2}{R}$

now we have

$mg = m*\frac{v^2}{R}$

now we have

$v^2 = Rg$

$v_{min} = \sqrt{Rg}$

so minimum speed will be given by above equation at the top point of the trajectory

Answer 2

Answer:

The answer of above question is √gR