The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius R and coefficient of static friction μ, is 

(1) $\mu Rg$

(2) $Rg\sqrt{\mu }$

(3) $\mu \sqrt{Rg}$

(4) $\sqrt{\mu Rg}$

Two carts of masses 200 kg and 300 kg on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the 200 kg cart travels a distance of 36 m and stops, then the distance travelled by the cart weighing 300 kg is 

(1) 32 m

(2) 24 m

(3) 16 m

(4) 12 m

Assuming the coefficient of friction between the road and tyres of a car to be 0.5, the maximum speed with which the car can move round a curve of 40.0 m radius without slipping, if the road is unbanked, should be 

(1) 25 m/s

(2) 19 m/s

(3) 14 m/s

(4) 11 m/s

Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is (g = 10 m/s²) 

(1) 30 m

(2) 40 m

(3) 72 m

(4) 20 m

On the horizontal surface of a truck (μ = 0.6), a block of mass 1 kg is placed. If the truck is accelerating at the rate of 5m/sec² then frictional force on the block will be 

(1) 5 N

(2) 6 N

(3) 5.88 N

(4) 8 N

A vehicle of mass m is moving on a rough horizontal road with momentum p. If the coefficient of friction between the tyres and the road be μ, then the stopping distance is 

(1) $\frac{\mathrm{p}}{2\mathrm{\mu mg}}$

(2) $\frac{{\mathrm{p}}^2}{2\mathrm{\mu mg}}$ 

(3) $\frac{\mathrm{p}}{2{\mathrm{\mu m}}^2\mathrm{g}}$

(4) $\frac{{\mathrm{p}}^2}{2{\mathrm{\mu m}}^2\mathrm{g}}$

                   
1. \(5.73~\text{m/s}^2\)
2. \(8.0~\text{m/s}^2\)
3. \(3.17~\text{m/s}^2\)
4. \(10.0~\text{m/s}^2\)

A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is given by

(1) $\left(1-\frac{1}{n^2}\right)$

(2) $\frac{1}{1-n^2}$

(3) $\sqrt{\left(1-\frac{1}{n^2}\right)}$

(4) $\sqrt{\frac{1}{1-n^2}}$

Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is 

(1) 0.33

(2) 0.25

(3) 0.75

(4) 0.80

A force of 750 N is applied to a block of mass 102 kg to prevent it from sliding on a plane with an inclination angle 30° with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are 0.4 and 0.3 respectively, then the frictional force acting on the block is 

(1) 750 N

(2) 500 N

(3) 345 N

(4) 250 N