A racing car completes 5 rounds of a circular track in 2 minutes. Find

1.	A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of π2/s2.
Answer» Given: 5 rounds = 2πr(5), t = 2minutes = 120s To find: Radius (r) Formula: a_cp = ω²r Calculation: From formula, a_cp = ω²r ∴ π² = \(\frac{V^2}{r}\) But v = \(\frac{2\pi r(5)}{t}=\frac{10\pi r}{t}\) ∴ π² = \(\frac{100 \pi^2 r^2}{rt^2}\) ∴ r = \(\frac{120\times120}{100}\) =144m The radius of the track is 144 m.

A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of π2/s2.

Answer»

Given: 5 rounds = 2πr(5),

t = 2minutes = 120s

To find: Radius (r)

Formula: a_cp = ω²r

Calculation: From formula,

a_cp = ω²r

∴ π² = \(\frac{V^2}{r}\)

But v = \(\frac{2\pi r(5)}{t}=\frac{10\pi r}{t}\)

∴ π² = \(\frac{100 \pi^2 r^2}{rt^2}\)

∴ r = \(\frac{120\times120}{100}\) =144m

The radius of the track is 144 m.