Angle of Repose

Q.

The coefficient of static friction between a block of mass m and an incline is ${\mu }_s$ = 0.3. What can be the maximum angle θ of the incline with the horizontal so that the block does not slip on the plane? (Also called angle of repose)

1. θ = cot^-1 (0.3)

2. θ = sin^-1 (0.3)

3. θ = cos^-1 (0.3)

4. θ = tan^-1 (0.3)

Q.

A block is placed on an inclined plane of inclination $\theta$. The angle of inclination is such that the block slides down the plane at a constant speed. The coefficient of kinetic friction between the block and the inclined plane is equal to

1. $sin\theta$

2. $cos\theta$

3. $tan\theta$

4. $cot\theta$

Q. A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${30}^{\circ }$, the box starts to slip and slides $4.0\text{m}$ down the plank in $4.0\text{s}$. The coeffficient of static and kinetic friction between the box and the plank will respectively be

1. $0.6$ and $0.5$
2. $0.5$ and $0.6$
3. $0.4$ and $0.3$
4. $0.6$ and $0.6$

Q. A cubical block rests on a plane of $\mu =\sqrt{3}$. The angle through which the plane be inclined to the horizontal so that the block just slides down will be

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

Q. A body is placed on an inclined plane. The coefficient of friction between the body and the plane is $\mu$. The plane is gradually tilted up. If $\theta$ is the inclination of the plane, then frictional force on the body is

1. decreases upto $\theta ={\tan }^{-1}\left(\mu \right)$ and constant after that
2. constant upto $\theta ={\tan }^{-1}\left(\mu \right)$ and decrease after that
3. Increases upto $\theta ={\tan }^{-1}\left(\mu \right)$ and constant after that
4. increases upto $\theta ={\tan }^{-1}\left(\mu \right)$and decrease after that

Q. For the arrangement shown in figure the tension in the string is [Given : ${\tan }^{-1}\left(0.8\right)={39}^{\circ }]$

1. $6\text{N}$
2. $6.4\text{N}$
3. $0.4\text{N}$
4. zero

Q. A block of mass $m$ is placed on a surface with a vertical cross section given by $y=\frac{x^3}{6}$. If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is

1. $\frac{1}{6}m$
2. $\frac{2}{3}m$
3. $\frac{1}{3}m$
4. $\frac{1}{2}m$

Q. A block rests on a rough plane whose inclination $\theta$ to the horizontal can be varied. Which of the following graphs indicates how the frictional force $F$ between the block and the plane varies as $\theta$ is increased?

1. 
2. 
3. 
4. 

Q. A block of mass $2\text{kg}$ 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 $0.7$. The frictional force on the block is

1. $9.8\text{N}$
2. $4.9\sqrt{3}\text{N}$
3. $19.6\text{N}$
4. $9.8\sqrt{3}\text{N}$

Q. A block of mass m is placed on a suface with a vertical cross section given by $y=\frac{x^3}{6}.$ If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is:

1. $\frac{1}{3}\text{m}$
2. $\frac{1}{2}\text{m}$
3. $\frac{1}{6}\text{m}$
4. $\frac{2}{3}\text{m}$