Question

A car takes a round turn of radius 50m with a velocity of 36 km/h. Calculate the centripetal acceleration of the car.

Answer 1

Centripetal force = mv²/r

centripetal acc. = F/m
=mv²/mr
=v²/r
=(36*5/18)²/50
=100/50
=2m/s²

Answer 2

Given :

• Radius of circular path = 50 m
• Velocity of car = 36 km/hr = 10 m/s

To Find :

• Centripetal acceleration

Formula used :

$Centripetal \: force \: = \dfrac{ {v}^{2} }{r}$

Solution :

We know,

$Centripetal \: force \: = \dfrac{m {v}^{2} }{r}$

And, Force = mass×acceleration

Acceleration = Force /mass

Hence,

$Centripetal \: acceleration = \dfrac{m {v}^{2} }{m \times r} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ {v}^{2} }{r}$

Now, on putting the required values we get

$Centripetal \: acceleration = \dfrac{ {10}^{2} }{50} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{100}{50} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \: m {s}^{ - 2}$

Therefore, the Centripetal acceleration of the car is 2 ms¯².