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.

Graph between the magnitude of relative velocity of the two car and time is `:`

Options

A.
B.
C.
D.

Answer

B

Explanation

At any moment of reaction velocity `v_(rel)=v_(A)-v_(B)`
It has same magnitude but different direction so
`v_(rel)=sqrt(v^(2)+v^(2)+2v^(2)cos (180-theta))`
`=sqrt(2v^(2)(1-cos theta))`
`v_(rel)=sqrt(v)sin ``(theta)/(2)`
`theta` change with time `t`