Q. The acceleration of a vehicle travelling with speed of $400{ms}^{- 1}$ as it goes round a curve of radius 160 m, is
A) $1\ {kms}^{- 2}$
B) $100{\ ms}^{- 2}$
C) $10\ {ms}^{- 2}$
D) $1\ {ms}^{- 2}$
Explanation
(a) $Given,\ \ v = 400\ {ms}^{- 1},\ r = 160\ m,a = ?$
$Centripetal\ force,\ \ F = \frac{{mv}^{2}}{r}$
$ma = \frac{{mv}^{2}}{r}$
$or\ \ \ \ a = \frac{v^{2}}{r}$
$So,\ \ \ a = \frac{(400)^{2}}{160} = \frac{{16 \times 10}^{4}}{160}$
$= 10^{3}\ {ms}^{- 2} = 1\ {kms}^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.