Coefficients of Friction

Q.

A football of radius $R$is kept on a hole of radius $r(𝑟<𝑅)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $\theta$ from the horizontal as shown in the figure below. The maximum value of $\theta$ so that the football does not start rolling down the plank satisfies (the figure is schematic and not drawn to scale)

1. $\sin \theta =\frac{r}{R}$

2. $\tan \theta =\frac{r}{R}$

3. $\sin \theta =\frac{r}{2R}$

4. $\cos \theta =\frac{r}{2R}$

Q. A pulley-block system is as shown in the figure. Blocks $2\text{kg}$ and $3\text{kg}$ are at rest. Coefficient of friction between $2\text{kg}$ and incline is

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

Q. The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of plane is given by

1. $2\tan \theta$
2. $\tan \theta$
3. $2\cot \theta$
4. $2\cos \theta$

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

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. 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. 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. $0.44$
3. $0.52$
4. $0.38$

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 circular road of radius 1000 m has banking angle ${45}^{\circ }$. The maximum safe speed of a car having mass 2000 kg will be, if the coefficient of friction between tyre and road is 0.5

1. 172 m/s
2. 124 m/s
3. 99 m/s
4. 86 m/s

Q. The ratio of time taken by a body to slide down a smooth surface to rough identical inclined surface of angle $\theta$ is $‘n^{\prime }$. Find the coefficient of friction.

1. $\frac{\tan \theta }{(1-n{)}^2}$
2. $\cot \theta (1-n^2)$
3. $\sin \theta (1-n^2)$
4. $\tan \theta (1-n^2)$

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. The ratio of time taken by a body to slide down a smooth surface to rough identical inclined surface of angle $\theta$ is $‘n^{\prime }$. Find the coefficient of friction.

1. $\frac{\tan \theta }{(1-n{)}^2}$
2. $\cot \theta (1-n^2)$
3. $\sin \theta (1-n^2)$
4. $\tan \theta (1-n^2)$

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

1. $0.5$
2. $0.4$
3. $0.6$
4. $0.2$

Q. The retarding acceleration of $4.9{\text{ms}}^{-2}$ due to frictional force stops the car of mass $400\text{kg}$ travelling on a road. The coefficient of friction between the tyre of the car and the road is

1. $0.7$
2. $0.5$
3. $0.4$
4. $0.3$

Q. In the figure shown, find the angle $\theta$ for which the pulling force is $\mu mg$ where $\mu$ is the coefficient of friction between the two surfaces

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

Q. The coefficient of friction can never be more than 1.

1. False
2. True

Q. A box of mass $\text{8 kg}$ is placed on a rough inclined plane of angle $\theta$ with horizontal. Its downward motion can be prevented by applying an upward pull $F$ and it can be made to slide upwards by applying a force $2F$. The coefficient of friction between the box and the inclined plane is

1. $\frac{\tan \theta }{3}$
2. $3\tan \theta$
3. $\frac{\tan \theta }{2}$
4. $2\tan \theta$

Q. Consider a car moving along a straight horizontal road with a speed of $72kmph$. If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is $(\text{Take}g=10\frac{m}{s^2})$

1. $30m$
2. $40m$
3. $72m$
4. $20m$

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. $\sqrt{F-\frac{L}{2}}$

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. Consider a $65kg$ ice skater is being pushed by two other with forces $F_1=26.4N$ and $F_2=18.6N$ as shown in the figure. If the coefficient of static friction is $0.04$ and coefficient of kinetic friction is $0.02$, which of the following option(s) is/are correct?
(Take $g=10m/s^2$)

1. Net force acting on the skater is $32.3N$.
2. Acceleration of the skater is $0.23m/s^2$.
3. Kinetic friction experienced by skater is $26N$.
4. Kinetic friction experienced by skater is $13N$.

Q. In the figure given below, blocks $1$ and $3$ are connected by a belt and block $2$ rests on the horizontal portion of the belt. When the three blocks are released from rest, they accelerate with a magnitude of $0.5{\text{m/s}}^2$. Block 1 has mass $m$, block 2 has mass $2m$ and block 3 has the same mass $2m$. What is the coefficient of kinetic friction between block 2 and the belt?
[Take $g=9.81{\text{m/s}}^2$ and assume the mass of the belt to be negligible]

1. 0.25
2. 0.37
3. 0.45
4. 0.67

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

1. $0.5$
2. $0.4$
3. $0.6$
4. $0.2$

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

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

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

1. $10{\text{ms}}^{-2}$
2. $5{\text{ms}}^{-2}$
3. $15{\text{ms}}^{-2}$
4. $0.5{\text{ms}}^{-2}$

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. Take $g=10m/s^2$

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

Q. Consider a car moving along a straight horizontal road with a speed of $72kmph$. If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is $(\text{Take}g=10\frac{m}{s^2})$

1. $30m$
2. $40m$
3. $72m$
4. $20m$

Q. A marble block of mass $2\text{kg}$ lying on ice when given a velocity of $6\text{m/s}$ is stopped by friction in $10\text{s}$. Then the coefficient of friction is

1. $0.01$
2. $0.02$
3. $0.03$
4. $0.06$