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. \(\frac{L}{L+l}\)

A system consists of three masses \(m_1,\) \(m_2,\) and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}.\) The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction \(=\mu.\)) The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is:
(Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.) 
                
1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \( \frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)

A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)

A block of mass \(1\) kg lying on the floor is subjected to a horizontal force given by, \(F=2\sin\omega t\) newtons. The coefficient of friction between the block and the floor is \(0.25\). The acceleration of the block will be:
1. positive and uniform
2. positive and non–uniform
3. zero
4. depending on the value of \(\omega\).$\mathrm{}$

A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction = \(\mu).\) A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec {F}\) where:
1. \(|{\vec {F}}| = mg+\mu mg\)
2. \(|\vec {F}| =\mu mg\)
3. \(|\vec {F}| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec{F}| = mg\)

A block is placed on a rough horizontal plane. A time dependent horizontal force, \(F=kt,\) acts on the block. The acceleration time graph of the block is :

1.		2.
3.		4.

The block of mass m (shown in the figure) does not move on applying the inclined force \(F\). The friction force acting on the block is:

                       
1. \(F \cos\theta\)
2. \(F \sin\theta\)
3. \(\mu mg-F \sin\theta\)
4. \(\mu mg\)

A conveyor belt is moving at a constant speed of \(2\) m/s. A box is gently dropped on it. The coefficient of friction between them is \(\mu = 0.5\). The distance that the box will move relative to the belt before coming to rest on it, taking \(g = 10\) ms^–2 is:

A \(40\) kg slab rests on a frictionless floor. A \(10\) kg block rests on top of the slab. The static coefficient of friction between the block and the slab is \(0.60\), while the kinetic coefficient of friction is \(0.40\). The \(10\) kg block is acted upon by a horizontal force of \(100\) N. If \(g =10 ~\text{m/s}^2,\) the resulting acceleration of the slab will be: