Maximum Push Using Friction

Q.

A body of mass 100 g is made just to slide on a rough surface by applying a force of 0.8 N. Find the coefficient of friction. Take g = 10 m/s².

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

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

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

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

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. A block of mass $m$ on a rough horizontal surface is acted upon by two forces as shown in figure. For equilibrium of block, the coefficient of friction between block and surface is

1. $\frac{F_1+F_2\sin \theta }{mg+F_2\cos \theta }$
2. $\frac{F_1\cos \theta +F_2}{mg-F_2\sin \theta }$
3. $\frac{F_1+F_2\cos \theta }{mg+F_2\sin \theta }$
4. $\frac{F_1\sin \theta -F_2}{mg-F_2\cos \theta }$

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

Q.

Calculate the couple on a cars steering wheel of diameters 40 cm. The force applied on each side is 2N.

Q. A body is sliding down a rough inclined plane of angle of inclination $\theta$ for which coefficient of friction varies with distance $y$ as $\mu \left(y\right)=Ky$, where $K$ is constant. Here $y$ is the distance moved by the body down the plane. The net force on the body is zero at $y=A$. Find the value of constant $K$.

1. $\frac{tan\theta }{A}$
2. $Acot\theta$
3. $\frac{cot\theta }{A}$
4. $Atan\theta$

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. A block of mass $m$ is placed on a prism of mass $M$. The inclined surface is smooth and inclination with horizontal is $\theta$. The horizontal surface is sufficiently rough to prevent slipping of prism. The body of mass $m$ is coming down the inclined face. Then

1. Acceleration of body along the inclined surface is $g\sin \theta$
2. Frictional force is $\frac{1}{2}mg\sin 2\theta$
3. Maximum frictional force is $\frac{mg}{2}$
4. Frictional force will be maximum when $\theta ={45}^{\circ }$

Q. What is the maximum value of the force $\text{F}$ such that the block shown in the arrangement, does not move ? (Take $g=10{\text{m/s}}^2$)

1. $20\text{N}$
2. $10\text{N}$
3. $12\text{N}$
4. $15\text{N}$

Q. If the coefficient of friction between $A$ and $B$ is $\mu$, the maximum acceleration of the wedge $A$ for which $B$ remains at rest with respect to the wedge is

1. $\mu g$
2. $g\left(\frac{1+\mu }{1-\mu }\right)$
3. $g\left(\frac{1-\mu }{1+\mu }\right)$
4. $\frac{g}{\mu }$

Q. As given in the figure two blocks $A$ & $B$ of weight $20\text{N}$ and $100\text{N}$ respectively are in equilibrium. These are being pressed against a wall by force $F$ as shown. If the coefficient of friction between the two blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by wall on block $B$ is $\left(f_2\right)$ and the frictional force applied by block $B$ on block $A$ is $\left(f_1\right)$.

1. $f_2=120\text{N}$
2. $f_2=150\text{N}$
3. $f_1=100\text{N}$
4. $f_1=20\text{N}$

Q. Block A, as shown in the figure weighs $2N$ and block B weighs $6N$. The coefficient of kinetic friction between all surfaces is 0.25. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, inextensible cord passing around a fixed, frictionless pulley.

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

Q. A block of mass $M$ is moving with a velocity $v$ on straight surface. What is the shortest distance and shortest time in which the block can be stopped if $\mu$ is coefficient of friction?

1. $\frac{v^2}{2\mu g},\frac{v}{\mu g}$
2. $\frac{v^2}{\mu g},\frac{v}{\mu g}$
3. $\frac{v^2}{2Mg},\frac{v}{\mu g}$
4. none of the above

Q. In the figure shown, what is the value of mass ‘$m$’ such that block $A$ slides up with a constant velocity. Take $g=10{\text{m/s}}^2$, Coefficient of friction between inclined plane and block $A$ is $0.5$.

1. $\text{1 kg}$
2. $\text{2 kg}$
3. $\text{3 kg}$
4. $\text{4 kg}$

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

Q. Two blocks each of mass $20\text{kg}$ are connected by an ideal string and this system is kept on rough horizontal surface as shown. Initially the string is just tight then a horizontal force $F=120\text{N}$ is applied on one block as shown.

If friction coefficient at every contact is $\mu =0.5$ then which of the following represents the correct free body diagram.

1. 
2. 
3. 
4. All of the above

Q. A block of mass $1kg$ starts moving at $t=0$ with speed $2m/s$ on rough horizontal surface with coefficient of friction $0.2$. A horizontal force $F$ is applied in the same direction of velocity which varies with time shown in figure (b). Find the speed of particle at $t=3s$ ($g=10m/s^2)$

1. $1m/s$
2. zero
3. $5m/s$
4. $2m/s$

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

Q. A block placed on a horizontal surface is being pushed by a force $F$ making an angle $\theta$ with the vertical as shown in figure. The coefficient of friction between block and surface is $\mu$. The force required to slide the block with uniform velocity on the floor is

1. $\frac{\mu mg}{(\sin \theta -\mu \cos \theta )}$
2. $\frac{(\sin \theta -\mu \cos \theta )}{\mu mg}$
3. $\mu mg$
4. None of these

Q. A block of mass $4kg$ is pressed against the wall by a force of $80N$ as shown in figure. Determine the value of friction force and acceleration of block respectively. (Take coefficient of static friction $0.2$, coefficient of kinetic friction $0.15$)

1. $8N,0m/s^2$
2. $32N,6m/s^2$
3. $8N,6m/s^2$
4. $32N,2m/s^2$

Q. A block placed on a horizontal surface is being pushed by a force $F$ making an angle $\theta$ with the vertical as shown in figure. The coefficient of friction between block and surface is $\mu$. The force required to slide the block with uniform velocity on the floor is

1. $\frac{\mu mg}{(\sin \theta -\mu \cos \theta )}$
2. $\frac{(\sin \theta -\mu \cos \theta )}{\mu mg}$
3. $\mu mg$
4. None of these

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

Q. Find the acceleration (in $m/s^2$) of the body of mass $20kg$ shown in the figure. Take $g=10m/s^2$.

1. $0.33$
2. $6.4$
3. $10$
4. $\text{Zero}$

Q. Two blocks $A$ and $B$ of mass $5\text{kg}$ and $2\text{kg}$, respectively, connected by a spring of force constant $=100\text{N/m}$ and are placed on an inclined plane of inclination ${30}^{\circ }$ as shown. If the system is released from rest then

1. There will be no compression or elongation in the spring, if all the surfaces are smooth.
2. There will be elongation in the spring, if $A$ is rough and $B$ is smooth.
3. Maximum elongation in the spring is $35\text{cm}$, if all surfaces are smooth.
4. There will be elongation in the spring, if $A$ is smooth and $B$ is rough.

Q. Two blocks each of mass $20\text{kg}$ are connected by an ideal string and this system is kept on rough horizontal surface as shown. Initially the string is just tight then a horizontal force $F=120\text{N}$ is applied on one block as shown.

If friction coefficient at every contact is $\mu =0.5$ then which of the following represents the correct free body diagram.

1. 
2. 
3. 
4. All of the above

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