Question

A racing car complete three rounds on a circular track in one minute .find the radius of the track if the car has uniform centripetal acceleration π^2/m^2​

Answer 1

Answer:

Explanation:

Angular velocity of the air:

ω=  

2×(60)

5×(2π)

​  

 

=  

12

π

​  

rad/sec

Centripetal acceleration is given by:

a  

c

​  

=πω  

2

 

Where r is the radius

∴ a  

c  =r×  

144 π  2 =π  2  

⇒r=144m

Answer 2

Answer:

$r=\frac{8100}{m^2}$

Explanation:

Considering 'm' as mass, which is constant.

Centripetal acceleration for circular motion is given by

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

Hence,

$\frac{\pi^2}{m^2}=\frac{v^2}{r}$

And, v = distance/time

∴ $v=\frac{2\pi r}{3*60}=\frac{\pi r}{90}$

Hence, in above equation,

$\frac{\pi^2}{m^2}=\frac{v^2}{r}\\\\r=(\frac{vm}{\pi})^2\\\\r=(\frac{\frac{\pi r}{90}m}{\pi})^2\\\\r=(\frac{mr}{90})^2\\\\r=\frac{m^2r^2}{(90)^2}\\\\8100=m^2r\\\\r=\frac{8100}{m^2}$