A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is u and is increasing at a rate α.
(a) The acceleration of the car is towards the centre of the path.
(b) The magnitude of the frictional force on the car is greater than mv2/r
(c) The friction coefficient between the ground and the car is not less than α/g.
(d) The friction coefficient between the ground and the car is μ = tan -1v2/rg
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(b) The magnitude of the frictional force on the car is greater than mv2/r
(c) The friction coefficient between the ground and the car is not less than α/g.
Explanation:
Since the circular motion is not uniform it will have both the radial and tangential components of acceleration and the resultant acceleration will be other than towards the center of path. Option (a) is wrong.
Since the car will experience a force equal to mv²/r radially outward so the friction force must be more than it to keep it on the circular path. Option (b) is correct.
Normal force on the car by the ground =mg . So frictional force on the car =µmg. It must not be less than outward force ma i.e. µmg≮ ma,
→µ≮ a/g. Option (c) is correct.
In limiting case µ=v²/rg, so option (d) is incorrect.