A block \(A\) with mass \(100~\text{kg}\) is resting on another block \(B\) of mass \(200~\text{kg}\). As shown in figure a horizontal rope tied to a wall holds it. The coefficient of friction between \(A\) and \(B\) is \(0.2\) while coefficient of friction between \(B\) and the ground is \(0.3\). The minimum required force \(F\) to start moving \(B\) will be: 

                   
1. \(900~\text{N}\)
2. \(100~\text{N}\)
3. \(1100~\text{N}\)
4. \(1200~\text{N}\)

A horizontal force of \(10\) N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \(0.2\). The weight of the block is: 

The coefficient of static friction, μ_s, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. (g = 10 m/s²) 

(1) 2.0 kg

(2) 4.0 kg

(3) 0.2 kg

(4) 0.4 kg

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. \(10.0~\text{m/s}^2\)