Rolling Friction

A disc of mass M and radius R is placed a rough horizontal surface with its axis horizontal. A light rod of length '2R' is fixed to the disc at point 'A' as shown in figure and a force `3/2` Mg is applied at the other end. If disc starts to roll without slipping the value of "10 × µ_min" where µ_min is minimum coefficient of friction between disc and horizontal surface required for pure rolling is ______.

A care is going at a speed of 21.6 km/hr when it encounters at 12.8 m long slope of angle 30° (in the following figure). The friction coefficient between the road and the tyre is `1/2sqrt3`. Show that no matter how hard the driver applies the brakes, the car will reach the bottom with a speed greater than 36 km/hr. Take g = 10 m/s².

A scooter starting from rest moves with a constant acceleration for a time ∆t₁, then with a constant velocity for the next ∆t₂ and finally with a constant deceleration for the next ∆t₃ to come to rest. A 500 N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is

In order to stop a car in shortest distance on a horizontal road, one should

Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional force on the vehicle by the road
(a) is towards east if the vehicle is accelerating
(b) is zero if the vehicle is moving with a uniform velocity
(c) must be towards east
(d) must be towards west.

Two cars of unequal masses use similar tyres. If they are moving at the same initial speed, the minimum stopping distance