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.

Which of the following statements is incorrect.

Options

A. Both car reaches the finishing line at same time.
B. Frictional force acting on the cars is directed towards centre whenever it acts
C. Frictional force have same magnitude for two car `'A'` and `'B'` during the trip.
D. none of these

Answer

C

Explanation

`(A)` Both have same linear speed at mean
When `A` at `A'` then `B` at `A'`
When `A` at `B` than `B` at `B'` When `A` at `C` then `B` at `C'`

`(B)` Friction for always towards centre to provide sufficient centripetal force `(mv^(2))/(r)`
`(C )` From above diagram

For car `A rarr O'` to `A fs =(mv^(2))/(r)`
For car `B rarr O' ` to `B ' fs' =( mv^(2))/(2r)=fs`
For `B rarr B'` to `C' =(mv^(2))/(r)=fs'`