Maximum Push Using Friction

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. 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 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. In the figure shown find the acceleration of $2\text{kg}$ body and also take ${\mu }_s=0.5$, ${\mu }_k=0.4$$[$Take $g=10{\text{m/s}}^2]$

1. $1.5{\text{m/s}}^2$
2. $1{\text{m/s}}^2$
3. $0.5{\text{m/s}}^2$
4. $0{\text{m/s}}^2$

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. $\text{Zero}$
4. $10$

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. In the figure shown, if the block does not slide down the plane when a force of $\text{10 N}$ is applied perpendicular to the plane, find the coefficient of static friction between the plane and the block.(Consider limiting case of friction) Take $g={\text{10 m/s}}^2.$

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

Q. The coefficient of static friction is $0.2$ between block $A$ of mass $2\text{kg}$ and the table as shown in the figure. 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. $2.0\text{kg}$
2. $4.0\text{kg}$
3. $0.2\text{kg}$
4. $0.4\text{kg}$

Q. A man of mass $60\text{kg}$ is pulling a mass $M$ by an inextensible light rope passing through a smooth and massless pulley as shown. $\mu$ between the ground and the man is $0.5$. Find the maximum value of $M$ that can be pulled slowly by the man without slipping on the ground.

1. $\frac{240}{2+\sqrt{3}}\text{kg}$
2. $\frac{120}{1+\sqrt{3}}\text{kg}$
3. $\frac{120}{2+\sqrt{3}}\text{kg}$
4. $\frac{120}{4+\sqrt{3}}\text{kg}$

Q. A block rests on a rough inclined 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. $2.5\text{kg}$
2. $1.6\text{kg}$
3. $2\text{kg}$
4. $4\text{kg}$