Coefficients of Friction

Q. A block of mass $10\text{kg}$ is kept on a rough inclined plane as shown in the figure. A force of $3\text{N}$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block does not move downward? $\text{(take}g=10{\text{ms}}^{-2})$

1. $32\text{N}$
2. $18\text{N}$
3. $23\text{N}$
4. $25\text{N}$

Q. A block of mass $10kg$ is placed on a rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of magnitude $100N$ is applied on the block, then acceleration of the block will be $[\text{Take}g=10m{s}^{-2}]$

1. $10m{s}^{-2}$
2. $5m{s}^{-2}$
3. $15m{s}^{-2}$
4. $0.5m{s}^{-2}$

Q. A block kept on a rough inclined plane, as shown in the figure remains at rest upto a maximum force $2\text{N}$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\text{N}$. The coefficient of static friction between the block and the plane is
(Take $g=10m/s^2)$

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

Q.

A body of mass 2 kg is lying on a rough inclined plane of inclination ${30}^{\circ }$.. Find the magnitude of the force parallel to the incline needed to make the block move (a) up the incline (b) down the incline, coefficient of static friction = 0.2

Q.

Find the mass M of the hanging block in figure whic will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the string and the pulleys are light.

Q.

Consider the situation shown in figure (8-E2). The system is released from rest and the block of mass 1.0 kg is found to have a speed 0.3 m/s after it has descended through a distance of 1 m. Find the coefficient of kinetic friction between the block and the table.

Q.

What happens to the coefficient of friction, when the weight of the body is doubled?

Q. A $20\text{kg}$ block is initially at rest on a rough horizontal surface. A horizontal force of $75\text{N}$ is required to set the block in motion. After it is in motion, a horizontal force of $60\text{N}$ is required to keep the block moving with constant speed. The coefficient of static friction is

1. $0.30$
2. $0.38$
3. $0.44$
4. $0.52$

Q. A spring block system (mass $m$, spring constant $k$) is placed on a smooth inclined plane of inclination $\theta$. The inclined plane is accelerated horizontally such that the block does not loose contact with the surface. The time period of small oscillation of the block is

1. $2\pi \sqrt{\frac{m}{k}}$
2. $2\pi \sqrt{\frac{msin\theta }{k}}$
3. $2\pi \sqrt{\frac{m}{ksin\theta }}$
4. $2\pi \sqrt{\frac{mg}{ka}}$

Q.

Figure( 6-E12) shows a small block of mass m kept at the left end of a larger block of mass M and length l. The system can slide on a horizontal road. The system is started towards right with an initial velocity v. The friction coefficientbetween the road and the bigger block is $\mu$ and that between the block is $\frac{\mu }{2}$. Find the time elapsed before the smaller blocks separates from the bigger block.

Q. A block of mass $m$, lying on a horizontal plane is acted upon by a horizontal force $P$ and another force $Q$, inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is
(Assume $P>Q$)

1. $\frac{(P\sin \theta -Q)}{(Mg-\cos \theta )}$
2. $\frac{(P-Q\sin \theta )}{(Mg+Q\cos \theta )}$
3. $\frac{(P\cos \theta +Q)}{(Mg-Q\cos \theta )}$
4. $\frac{(P+Q\sin \theta )}{(Mg+Q\cos \theta )}$

Q.

A block is at rest on an inclined plane making an angle αwith the horizontal. As the angle αof the incline is increased, the block starts slipping when the angle of inclination becomes θ. The coefficient of static friction between the block and the surface of the inclined plane is or
A body starts sliding down at an angle θto horizontal. Then coefficient of friction is equal to

1. sinθ

2. cosθ

3. tanθ

4. Independent of θ

Q. For a body on a horizontal surface, coefficients of static and kinetic frictions are $0.4$ and $0.2$, respectively. When the body is in uniform motion on the surface, a horizontal force equal in magnitude to limiting friction is applied on it. The acceleration produced is

1. $0.4\text{g}$
2. $0.1\text{g}$
3. $0.2\text{g}$
4. $0.6\text{g}$

Q.

A block of mass m is placed on a triangular block of mass M, which in turn is placed on a horizontal surface as shown in figure (9-E21). Assuming frictionless surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.

Q.

The time taken by a body to slide down a rough ${45}^{\circ }$ inclined plane is thrice of that is required to slide down a smooth ${45}^{\circ }$ inclined plane. The coefficient of kinetic friction between the object and rough plane is given by:

1. $\frac{3}{4}$
2. $\sqrt{\frac{3}{4}}$
3. $\sqrt{\frac{2}{4}}$
4. $\frac{8}{9}$

Q. A charged particle having charge $q$ and mass $m$ is projected into a region of uniform electric field of strength $\overrightarrow{E_0}$, with velocity $\overrightarrow{V_0}$ perpendicular to $\overrightarrow{E_0}$. Throughout the motion, apart from electric force, the particle also experiences a dissipative force of constant magnitude $q{E}_0$ and directed opposite to its velocity. If $\overrightarrow{V_0}|=6\text{m/s}$, then find its speed when it has turned through an angle of ${90}^{\circ }$.

Write speed in m/s.

Q.

A block pressed against the vertical wall is in equilibrium. The minimum coefficient of friction is

1. $0.4$
2. $0.2$
3. $0.5$
4. None of these

Q. A block begins to slide down a rough inclined plane of angle ${45}^{\circ }$ and moves $1m$ in $\sqrt[4]{42}\text{second}$. What is the coefficient of friction between the plane and the block? $g=10m/s^2$

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.8$

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

1. 20%
2. 25%
3. 35%
4. 15%

Q.

A body is projected along a rough horizontal surface with a velocity of $6m/s$. If the body comes to rest after traveling a distance of $9m$, the coefficient of sliding friction is ($g=10m{s}^2$)

Q. A rough vertical board has an acceleration $a$ so that a $2kg$ block pressing against it does not fall. The coefficient of friction between the block and the board is $\mu$. Then,

1. $\mu >\frac{g}{a}$
2. $\mu <\frac{g}{a}$
3. $\mu <\frac{a}{g}$
4. $\mu >\frac{a}{g}$

Q. A body is moving along a rough horizontal surface with an initial velocity $6m/s$. If the body comes to rest after travelling $9m$, then the coefficient of sliding firction will be

1. $0.4$
2. $0.2$
3. $0.6$
4. $0.8$

Q. The block shown in the figure is just on the verge of slipping. The coefficient of static friction between the block and table is

Q.

Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2

1. 0.14 m/s

2. 140 m/s

3. 1.4 km/s

4. 14 m/s

Q.

Which of the following has the greatest value of coefficient of friction?

1. Static friction

2. Rolling friction

3. Sliding friction

4. Fluid friction

Q. The time taken by a body to slide down a rough ${30}^{\circ }$ inclined plane is twice of that required to slide down a smooth ${30}^{\circ }$ inclined plane. The coefficient of kinetic friction between the object and the rough plane is given by

1. $\frac{8}{9}$
2. $\sqrt{\frac{3}{4}}$
3. $\sqrt{\frac{2}{4}}$
4. $\frac{\sqrt{3}}{4}$

Q. In the arrangement shown in figure. There is a fricion force between the block of masses $m$ and $2m$. Block of mass $2m$ is kept on a smooth horizontal plane. The mass of suspended block is $m$. Block $A$ is stationary with respect to block of mass $2m$. The minimum value of coefficient of fricion betwen $A$ and $B$ is

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

Q. A body of mass $8\text{kg}$ lies on a rough horizontal table. It is observed that a certain horizontal force gives the body an acceleration of $4{\text{ms}}^{-2}$. When this force is doubled, the acceleration of the body is $16{\text{ms}}^{-2}$. The coefficient of friction is

1. 0.2
2. 0.3
3. 0.4
4. 0.8

Q.

A block of mass m slips on a rough horizontal table under the action of a horizontal force applied to it. The coefficient of friction between the block and the table is $\mu$ the table does not move on the floor. Find the total frictional force appied by the floor on the legs of the table. Do you need the friction coefficient between the table and the floor or the mass of the table?

Q. A chain of mass per unit length $\lambda =2\text{kg/m}$ is pulled up by a constant force $F$. Initially, the chain is lying on a rough surface and passes onto the smooth surface. The co-efficient of kinetic friction between chain and rough surface is $\mu =0.1$. The length of the chain is $L$. Then, find the speed ($\text{in m/s}$) of the chain when $x=L$. Take $g=10{\text{m/s}}^2$.

1. $\sqrt{F-L}$
2. $\sqrt{F-2L}$
3. $\sqrt{F-4L}$
4. $\sqrt{F-\frac{L}{2}}$