The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t = 0. Calculate the velocity v of the block when t= 0.4s. The coefficient of kinetic fricton is ${\mu }_k=0.3$. [This question includes concepts from Work, Energy & Power chapter]

1. 0.6 m/s

2. 1.2 m/s

3. 1.8 m/s

4. 2.4 m/s

Two balls of masses m₁ and m₂ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass m₁ travels a distance s₁ and stops. If the coefficients of friction between the balls and ground are same, the mass m₂ stops after travelling the distance 

1. $s_2=\frac{m_1}{m_2}{s}_1$

2. $s_2=\frac{m_2}{m_1}{s}_1$

3. $s_2=\frac{m_1^2}{m_2^2}{s}_1$

4. $s_2=\frac{m_2^2}{m_1^2}{s}_1$

A block \(B\) is placed on top of block \(A\). The mass of block \(B\) is less than the mass of block \(A\). Friction exists between the blocks, whereas the ground on which block \(A\) is placed is assumed to be smooth. A horizontal force \(F\), increasing linearly with time begins to act on \(B\). The acceleration \(a_A\) and \(a_B\) of blocks \(A\) and \(B\) respectively are plotted against \(t\). The correctly plotted graph is:

1.		2.
3.		4.

A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l₁ of the part of this rope which can overhang from the edge of the table without sliding down is 

1. $\frac{l}{\mu }$

2. $\frac{l}{\mu +l}$

3. $\frac{\mu l}{1+\mu }$

4. $\frac{\mu l}{\mu -1}$

A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang over one edge of the table is 

1. 20%

2. 25%

3. 35%

4. 15%

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. \(\dfrac{l}{L}\)
2. \(\dfrac{l}{L+l}\)
3. \(\dfrac{l}{L-l}\)
4. \(\dfrac{L}{L+l}\)

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: