Angle of Friction

Q. A force of $100N$ is applied on a mass of $3kg$ as shown in the figure. The coefficient of friction between the surface and the block is $\mu =\frac{1}{\sqrt{3}}$. The frictional force acting on the block is

1. $15N$ downwards
2. $30N$ upwards
3. $20N$ downwards
4. $25N$ upwards

Q.

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

1. 

2. 

3. 

4. 

Q.

Which of the following is correct

1. Angle of friction is defined as the angle between the normal reaction force and the resultant force of normal reaction force and friction when an object just begins to move.

2. Angle of repose is defined as the minimum angle of an inclined plane which causes an object to slide down the plane.

3. Angle of friction is defined as the minimum angle of an inclined plane which causes an object to slide down the plane.

4. Angle of repose is defined as the angle between the normal reaction force and the resultant force of normal reaction force and friction when an object just begins to move.

Q.

A rod of mass m is supported on a wedge of mass M as shown in figure. Find the accelerations of rod a and wedge A in the arrangement. Assume that the friction between all contact surfaces is negligible.

1. $A=\frac{Mg}{(mtan\alpha +Mcot\alpha )}$

2. $A=\frac{Mg}{(msin\alpha +Mcot\alpha )}$

3. $a=\frac{mgtan\alpha }{(mtan\alpha +mcot\alpha )}$

4. $a=\frac{Mgtan\alpha }{(Msin\alpha +Mcot\alpha )}$

Q. If coefficient of friction between all surfaces is 0.4, then find the minimum force $F$ required to just keep the system from moving.
[Take $g=10{\text{m/s}}^2$]

1. $62.5\text{N}$
2. $150\text{N}$
3. $135\text{N}$
4. $50\text{N}$

Q.

A varying horizontal force F=at acts on a block of mass m kept on a smooth horizontal surface. An identical block is kept on the first block. The coefficient of friction between the blocks is µ. The time after which relative sliding between the blocks prevails is:

(a) 2mg/a (b) 2µmg/a (c) µmg/a (d) 2µmga

Q.

A body takes just twice the time as long to slide down a plane inclined at ${30}^o$ to the horizontal as if the plane were friction less. The coefficient of friction between the body and the plane is

1. 

2. 

3. 

4. 

Q. Block A of weight 100 N rests on a frictionless inclined plane of slope angle ${30}^{\circ }$. A flexible rope attached to A passes over a pulley and is connected to block B of weight B. The weight W (in N, correct upto two decimal place ) for which system is in equilibrium is____.

1. 50

Q. How does friction exist ?

Q. A force of $30\text{N}$ is sufficient just to pull a block of mass $4\text{kg}$, horizontally over a flat rough surface. The angle of friction is

1. ${45}^{\circ }$
2. ${53}^{\circ }$
3. ${37}^{\circ }$
4. ${30}^{\circ }$

Q. A body of mass $2\text{kg}$ is kept on a rough horizontal surface. If ${\mu }_s=0.5$ and an external force of $F=5\text{N}$ is applied on the body, find the angle of friction.
(Take $g=10{\text{m/s}}^2$)

1. ${\tan }^{-1}\left(\frac{1}{2}\right)$
2. ${\tan }^{-1}\left(2\right)$
3. ${\cot }^{-1}\left(2\right)$
4. ${\cot }^{-1}\left(\frac{1}{2}\right)$

Q. For small applied force, the slope of graph between friction and applied force is

1. 30 degrees
2. 45 degrees
3. 60 degrees
4. dependent on the coefficient of static friction.

Q. The coefficient of friction has no unit.

1. False
2. True

Q. A body of mass $2\text{kg}$ is kept on a rough horizontal surface. If ${\mu }_s=0.5$ and an external force of $F=5\text{N}$ is applied on the body, find the angle of friction.
(Take $g=10{\text{m/s}}^2$)

1. ${\tan }^{-1}\left(2\right)$
2. ${\cot }^{-1}\left(\frac{1}{2}\right)$
3. ${\tan }^{-1}\left(\frac{1}{2}\right)$
4. ${\cot }^{-1}\left(2\right)$

Q. A block is moving on an inclined plane making an angle 45° 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

Q. Assertion :The coefficient of friction can be greater than unity. Reason: The force of friction is dependent on normal reaction and the ratio of force of friction and normal reaction cannot exceed unity.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect and Reason is correct

Q. A force $\overrightarrow{F}=(2\hat{i}+3\hat{j})N$ acts ona particle and displaces it form initial position $\overrightarrow{x_1}=(3\hat{i}+4\hat{j})m$ to final position $\overrightarrow{x_2}=(2\hat{i}+3\hat{j})m$, then work done by force, is

1. $-19J$
2. $-5J$
3. $12J$
4. $19J$

Q. Two bodies having same mass, $2$ $kg$ each, have different surface area $50m^2$ and $100m^2$ in contact with a horizontal plane. If the coefficient of friction is $0.2$, the ratio of frictional forces that come into play when the bodies are in motion, will be:

1. $1:2$
2. $1:1$
3. $2:1$
4. $1:4$

Q. An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the surface and the insect is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with vertical, the maximum possible value of $\alpha$ is given by :

1. $\cot \alpha =3$
2. $\tan \alpha =3$
3. $cosec\alpha =3$
4. $\sec \alpha =3$

Q. If a raw egg and a boiled egg are spinned together with same angular velocity on the horizontal surface then which one will stops first?

1. boiled egg
2. raw egg
3. Both egg will stop simultaneously
4. Cannot be ascertained

Q. The magnitude and direction of the force of friction acting on A are

1. mg, down the plane
2. $\frac{mg}{2}$, up the plane
3. $\frac{mg}{\sqrt{2}}$, up the plane
4. $\frac{mg}{3\sqrt{2}}$, down the plane

Q. A block of mass 15 kg is placed on a long trolley The coefficient of friction between the block and trolley is 0. 18 The trolley accelerates with 0.5 m/$s^2$ for 20 s then what is the friction force

1. 133.3 N
2. 7.5 N
3. 3.5 N
4. N.O.T

Q.

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

1. $cot\alpha =3$

2. $tan\alpha =3$

3. $sec\alpha =3$

4. $cosec\alpha =3$

Q. A block of mass 4 kg is kept on a rough horizontal surface. A horizontal force of 19.6 N is just able to slide the block.
In a force of 16 N acts then what is the frictional force acting on the block?

1. 16 N
2. 3.6 N
3. 19.6 N
4. can't predict as the value of coefficient of kinetic friction is not given

Q. If co-efficient of friction is $\sqrt{3}$ then what will be the angle between two surfaces?

Q. Assertion :A body on an inclined plane just tends to slide down if the angle of inclination is equal to angle of friction. Reason: When the angle of inclination is equal to the angle of friction, the component of weight parallel to the plane is just sufficient to overcome the frictional force.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by:

1. $\cos \alpha =3$
2. $\tan \alpha =3$
3. $\cot \alpha =3$
4. $\cos \sec \alpha =3$

Q. The coefficient of friction g and the angle of friction A are related as

1. $sin\lambda =\mu$
2. $cos\lambda =\mu$
3. $tan\lambda =\mu$
4. $tan\mu =\lambda$

Q. A force of $7kgwt$ is sufficient to pull a block of $10kgwt$ over a flat surface. What is the angle of friction?

Q. An insect crawls up a hemispherical surface very slowly as shown in figure. The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by

1. $cot\alpha =3$
2. $sec\alpha =3$
3. $cosec\alpha =3$
4. none