Coefficients of Friction

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

1. False
2. True

Q.

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

1. 

2. 

3. 

4. 

Q. For any given pair of surfaces, the coefficient of friction is maximum in case of limiting friction.

1. False
2. True

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 ${30}^0$, the box starts to slip and slides $4m$ down the plank in $4s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively

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

Q. A body of mass $m$ is launched up a rough inclined plane of angle ${45}^{\circ }$ with the horizontal. If the time of ascent is half the time of descent, the coefficient of friction is

1. $\frac{2}{5}$
2. $\frac{3}{5}$
3. $\frac{3}{4}$
4. $\frac{5}{8}$

Q. The coefficient of friction has no unit.

1. False
2. True

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. 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 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. A circular smooth road of radius $r=20m$ is banked for vehicles moving at a speed of $v=36kmph$. If the friction coefficient between the road and the road and the Tyre is $0.3$, find the maximum speed of a vehicle going around this curved road.

1. $29.39kmph$
2. $39.29kmph$
3. $40.39kmph$
4. None of these

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. 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. Two inclined friction less tracks, one gradual and the other steep meet at $A$ from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given ${\theta }_1={30}^0,{\theta }_2={60}^0$, and $h=10m$, what are the speeds and times taken by the two stones ?

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. 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 $20\text{kg}$ 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 $10kg$ 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 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. 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 $m$, 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. 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. 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. Starting from rest, a body slides down a ${45}^{\circ }$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of kinetic friction between the body and the inclined plane is

1. $0.33$
2. $0.25$
3. $0.75$
4. $0.80$

Q. Figure shows two blocks tied by a string. A variable force $F=5t$ is applied on the block A. The coefficient of friction for the blocks A and B are $0.5$ and $0.6$ respectively. Find the tension in the string at time $t=2\text{sec}$ (in newtons)

Q. A body of mass $m$ is launched up a rough inclined plane of angle ${45}^{\circ }$ with the horizontal. If the time of ascent is half the time of descent, the coefficient of friction is

1. $\frac{2}{5}$
2. $\frac{3}{5}$
3. $\frac{3}{4}$
4. $\frac{5}{8}$

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. $\frac{(P+Q\sin \theta )}{(Mg+Q\cos \theta )}$