Two racing cars `'A'` and `'B'` having masses `'M'` and `'2m'` respectively start running from the starting line on a horizontal plane.Both cars `'A'` and `B'` have same speed `'V'` which is constant through out the journey. The track of the two cars are the arcs of concentric circle having centres `O_(1)` and `O_(2)` as shwon in figure with data. The friction coefficient of the two cars with the road is same. There is a finishing line at the end of the arc. Using these informations solve the following questions.

The time interval during which the two cars have same angular speed `:`

Options

A. Always along the motion
B. Never
C. `(2pir)/(V)`
D. `(4pir)/(V)`

Answer

C

Explanation

For same angular speed `omega`
`w=(2pi n)/(t_(1))`
`n:` fractional revelutinar number of revolution
For `'A'n=1//4`
`w=(2pi(1//4))/(t_(1)),w=((v)/(r))`
`(v)/(r)=(pi)/(2t_(1)) ......(i)`
For `B` car `t_(1)=((pir)/(2v))`
`w=(2pir)/(t_(2))=((pi)/(4t_(2)))=((v)/(2r))`
`(v)/(r)=((pi)/(2t_(2)))` So time interval for equal angular velocity
`rArr Deltat=((pir)/(2v))=t_(1)=t_(2)`.