Q. 5

# A car of mass M i

Since the car is moving on a horizontal circular path, the direction of its velocity is changing at each point along the path and there is an acceleration towards the centre. But it is also given that there is a tangential/translational acceleration ‘a’ present. Therefore, net acceleration cannot be towards the centre. This implies, (A.) is incorrect.

The car is moving on a circular path in an accelerated motion, there is a centrifugal force acting on it pushing it in the outwards direction. To keep the car on the path there must be a frictional force acting on the car which is at least equal to this force or greater.

This would imply, frictional force ≥ force acting on the car

f≥Mv2/r

μMg≥Mv2/r

μ≥Mv2/Mrg

μ≥v2/rg

μ≥a/g

Options (B) and (C) are correct.

The condition given in option (D) is the condition for an elevated road, i.e. banking of road but the circular path given in the question is horizontal. Therefore, this condition is not applicable here.

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