The radius of the curvature will be 1.49 m. Because to balance the passengers safely, acceleration due to gravity (mg) should be equally balanced by centripetal force (Fc).
What is Centripetal force?
The force applied to an item in curved motion that is pointed toward the axis of rotation or the centre of curvature is known as a centripetal force.
[tex]F = \frac{Mv^{2}}{r}[/tex]
What is acceleration?
It is a vector quantity that can be described as the speed at which an object changes its speed. When an object's velocity changes, it is said to be accelerating.
What are the calculations?
[tex]F_{c} = m a_{c} \\mg = ma_{c} \\g = a_{c} \\9.8 m/s = a_{c} \\V = 12 m/s (given)\\a_{c} = \frac{V^{2} }{r} * r\\V = \sqrt{a_{c} r } \\12 m/s = \sqrt{9.8* r} \\\frac{12}{9.8} ^{2} = r\\\\1.49 m = r[/tex]
Hence, the radius of the curvature will be 1.49 m.
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