A uniform chain of length \(L\) hangs partly from a table which is kept in equilibrium by friction. If the maximum length that can be supported without slipping is \(l,\) then the coefficient of friction between the table and the chain is: 
1. \(\frac{l}{L}\)
2. \(\frac{l}{L+l}\)
3. \(\frac{l}{L-l}\)
4. \(\frac{L}{L+l}\)

When two surfaces are coated with a lubricant, then they 

(1) Stick to each other

(2) Slide upon each other

(3) Roll upon each other

(4) None of these

A 20 kg block is initially at rest on a rough horizontal surface. A horizontal force of 75 N is required to set the block in motion. After it is in motion, a horizontal force of 60 N is required to keep the block moving with constant speed. The coefficient of static friction is 

(1) 0.38

(2) 0.44

(3) 0.52

(4) 0.60

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

A block of mass 50 kg can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is 0.6. The least force of pull acting at an angle of 30° to the upward drawn vertical which causes the block to just slide is 

(1) 29.43 N

(2) 219.6 N

(3) 21.96 N

(4) 294.3 N

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