Maximum Push Using Friction

Q. A block rests on a rough incline plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in $\text{kg}$ ) is (take $g=10{\text{m/s}}^2)$

1. $2.5$
2. $4.0$
3. $2.0$
4. $1.6$

Q. A block of mass $2\text{kg}$ is put on a rough horizontal surface having coefficient of friction $0.5$. The acceleration of block and frictional force acting on block if $F=5\text{N}$ is (Take $g=10{\text{m/s}}^2$)

1. $\frac{5}{2}{\text{m/s}}^2,10\text{N}$
2. $0{\text{m/s}}^2,5\text{N}$
3. $0{\text{m/s}}^2,10\text{N}$
4. $5{\text{m/s}}^2,5\text{N}$

Q. The coefficient of static friction, ${\mu }_s$, between block $A$ of mass 2 kg and the table as shown in the figure is $\mathrm{0.2.}$ 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. $(g=10{\text{m/s}}^2)$

1. 0.2 kg
2. 0.4 kg
3. 2.0 kg
4. 4.0 kg

Q. A block is moving on an inclined plane making an angle ${45}^{\circ }$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $n=10\mu$, then $n$ is

1. $2$
2. $6$
3. $4$
4. $5$

Q. Find the minimum value of coefficient of friction between the $4\text{kg}$ block and the surface for the system to be at rest for the figure shown, (Block $A=4\text{kg}$ and block $B=3\text{kg}$)

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.75$

Q. A car starts from rest to cover a distance $s$. The coefficient of friction between the road and the tyres is $\mu$. The minimum time in which the car can cover the distance is proportional to

1. $\mu$
2. $\frac{1}{\mu }$
3. $\sqrt{\mu }$
4. $\frac{1}{\sqrt{\mu }}$

Q. A body of mass $10\text{kg}$ is lying on a rough plane inclined at an angle of ${30}^{\circ }$ to the horizontal and the co-efficient of friction is $0.5$. The minimum force required to pull the body up the plane is ($g=9.8{\text{m/s}}^2$)

1. $914\text{N}$
2. $91.4\text{N}$
3. $9.14\text{N}$
4. $0.914\text{N}$

Q. A block of mass 5 kg is kept over a rough horizontal surface. A time varying force acts on it along the horizontal given by F = 2t. The block starts slipping at t = 2.5 s and its acceleration at t = 3 s is $0.4{\text{m/s}}^2$. The summation of coefficients of static and kinetic friction is (take $g=10{\text{ms}}^{-2}$)

Q. A block of mass $1\text{kg}$ is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown. Another block of $1\text{kg}$ is connected to the other end of the string. The acceleration of the system is (coefficient of friction for rough horizontal surface is $\mu =0.2$)

1. $0.8\text{g}$
2. Zero
3. $0.4\text{g}$
4. $0.5\text{g}$

Q. For the arrangement shown in figure, the tension in the string to prevent it from sliding down is

1. $64\text{N}$
2. $6\text{N}$
3. $0.4\text{N}$
4. None of these

Q. A block of mass $10\text{kg}$ is pressed against a vertical wall. If the coefficient of friction between the wall and the block is $0.2$, then what is the minimum force that should be applied on the block so that does not fall to the ground?

1. $600\text{N}$
2. $500\text{N}$
3. $400\text{N}$
4. $555.5\text{N}$

Q. A uniform rope of length $l$ lies on a table. If the coefficient of friction is $\mu$, then the maximum length $l_1$ of the hanging part of the rope which can overhang from the edge of the table without sliding down is

1. $\frac{l}{\mu }$
2. $\frac{1}{(\mu +1)}$
3. $\frac{\mu l}{(\mu +l)}$
4. $\frac{\mu l}{(\mu -1)}$

Q. $\text{Statement I:}$ It is easier to pull a heavy object than to push it on a level ground.

$\text{Statement II:}$ The magnitude of frictional force depends on the nature of the two surfaces in contact.

1. Both $\text{Statements}$ are true and $\text{Statement II}$ is the correct explanation for $\text{Statement I}$.
2. Both $\text{Statements}$ are true and $\text{Statement II}$ is not the correct explanation for $\text{Statement I}$.
3. $\text{Statement I}$ is true and $\text{Statement II}$ is false.
4. $\text{Statement I}$ is false and $\text{Statement II}$ is true.

Q. A time dependent force $F=3t$ ($F$ in Newtons and $t$ in seconds) acts on three blocks $m_1,m_2$ and $m_3$ kept in contact on a rough ground as shown. Coefficient of friction between blocks and ground is $0.4$. If $m_1,m_2$ and $m_3$ are $3kg,2kg$ and $1kg$ respectively, the time after which the blocks start to move is $(g=10m{s}^{-2})$

1. $4sec$
2. $8sec$
3. $\frac{8}{3}sec$
4. $\frac{4}{3}sec$

Q. The coefficient of friction between the tyres and road is $0.4$. The minimum distance covered before attaining a speed of $8{\text{ms}}^{-1}$ starting from rest is nearly $(g=10m/s^2)$

1. 8.0 m
2. 4.0 m
3. 10.0 m
4. 16.0 m

Q. A piece of ice starting from rest slides down a rough ${45}^{\circ }$ incline in twice the time it takes to slide down a frictionless ${45}^{\circ }$ incline. What is the coefficient of friction between the ice and incline?

1. $0.50$
2. $0.75$
3. $0.40$
4. $0.25$

Q. A block of mass $15\text{kg}$ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has a tension of $50\text{N}$. Calculate the coefficient of friction between the block and inclined plane. Consider $g=10{\text{ms}}^{-2}$

Q. A block is placed on a rough horizontal plane. A time dependent horizontal force $F=kt$ acts on the block. Here $k$ is a positive constant. Acceleration-time graph of the block is

1. 
2. 
3. 
4. 

Q. A solid uniform disc of mass m rolls without slipping down an inclined plane with an acceleration a. The frictional force on the disc due to surface of the plane is

1. $2ma$
2. $\frac{3}{2}ma$
3. $ma$
4. $\frac{1}{2}ma$

Q. Two blocks $A$ and $B$ are arranged as shown in the figure. The mass of block $A$ is $10\text{kg}$. The coefficient of friction between block $A$ and the horizontal plane is $0.2$. The minimum mass of block $B$ to start motion will be

1. $5\text{kg}$
2. $0.2\text{kg}$
3. $10\text{kg}$
4. $2\text{kg}$

Q. A mass M is suspended from a massless spring. An additional mass m stretches the spring further by a
distance x. The combined mass will oscillate with a period

1. $2\pi \sqrt{\left\{\frac{(M+m)x}{mg}\right\}}$
2. $2\pi \sqrt{\left\{\frac{mg}{(M+m)x}\right\}}$
   
3. $\frac{\pi }{2}\sqrt{\left\{\frac{mg}{(M+m)x}\right\}}$
4. $2\pi \sqrt{\left\{\frac{(M+m)}{mgx}\right\}}$
   

Q. A body of mass $m$ rests on a horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between the body and surface will be

1. $\mu [mg-\left(\frac{P}{2}\right)]$
2. $\mu mg$
3. $\mu [mg+\left(\frac{P}{2}\right)]$
4. $\mu [mg-\left(\frac{\sqrt{3}P}{2}\right)]$

Q. A person wants to drive on the vertical surface of a large cylindrical wooden 'well' commonly known as death well' in a circus. The radius of the well is R and the coefficient of friction between the tyres of the motorcycle and the wall of the well is ${\mu }_s$. The minimum speed, the motorcycle must have in order to prevent slipping, should be

1. $\sqrt{\frac{{\mu }_s}{Rg}}$
2. $\sqrt{\frac{{\mu }_{s}g}{R}}$
3. $\sqrt{\frac{Rg}{{\mu }_s}}$
4. $\sqrt{\frac{R}{{\mu }_{s}g}}$

Q. A block of mass $1kg$ is kept on a rough inclined plane of angle ${30}^{\text{o}}$. Find the frictional force acting on the block. Given coefficient of friction $\mu =0.8$

1. $6.7\text{N}$
2. $4.9\text{N}$
3. $10\text{N}$
4. Zero

Q. A block of mass $m$ is placed on the top of another block of mass $M$ as shown in the figure. The coefficient of friction between them is $\mu$. Maximum acceleration of $M$ such that $M$ and $m$ move together is (there is no friction between ground and $M$)

1. $\mu g$
2. $\frac{g}{\mu }$
3. $\frac{g}{{\mu }^2}$
4. $\frac{{\mu }^2}{g}$

Q. The brakes of a car moving at $20m/s$ along a horizontal road are suddenly applied and it comes to rest after travelling some distance. If the coefficient of friction between the tyres and the road is $0.90$, and it is assumed that all four tyres behave identically, find the shortest distance the car would travel before coming to a stop.

1. $2.22m$
2. $11.35m$
3. $22.2m$
4. $4.54m$

Q. The pulley is given an acceleration $a_0=2{\text{m/s}}^2$ starting from rest. A cable is connected to a block $A$ of mass $50\text{kg}$ as shown. Neglect the mass of the pulley. If $\mu =0.3$ between the block and the floor, then the tension in the cable is:

1. $200\text{N}$
2. $250\text{N}$
3. $300\text{N}$
4. $350\text{N}$

Q. The tension $T$ in the string shown in figure is

1. Zero
2. $35\sqrt{3}\text{N}$
3. $50\text{N}$
4. $(\sqrt{3}-1)50\text{N}$

Q. The block $\text{B}$ has a mass of $10\text{kg}$. The coefficient of friction between block $\text{B}$ and the surface is $\mu =0.5$. Determine the acceleration of the block $\text{A}$ of mass $16\text{kg}$. Neglect the mass of the pulleys and cords. (Take $g=10{\text{m/s}}^2)$.

1. Zero
2. $1{\text{m/s}}^2$
3. $2{\text{m/s}}^2$
4. None of these

Q. A block of mass $2\text{kg}$ is put on a rough horizontal surface having coefficient of friction $0.5$. The acceleration of block and frictional force acting on block if $F=5\text{N}$ is (Take $g=10{\text{m/s}}^2$)

1. $\frac{5}{2}{\text{m/s}}^2,10\text{N}$
2. $0{\text{m/s}}^2,5\text{N}$
3. $0{\text{m/s}}^2,10\text{N}$
4. $5{\text{m/s}}^2,5\text{N}$