Calculating Friction Using Coeffcients

Q. The upper half of an inclined plane with inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, then the coefficient of kinetic friction for the lower half is given by

1. $\text{2 tan}\theta$
2. $\text{tan}\theta$
3. $\text{2 sin}\theta$
4. $\text{2 cos}\theta$

Q. A horizontal force of 10 N in necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is

1. 2 N
2. 20 N
3. 50 N
4. 100 N

Q. Starting from rest, a body slides down a ${45}^{\circ }$ rough inclined plane in twice the time it takes to slide down the same distance in the absence of friction (with same inclination). The coefficient of friction between the body and the inclined plane is

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

Q. Given in the figure are two blocks A and B of weight $20N$ and $100N$ respectively. The blocks are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block B and the wall is $0.15$, the frictional force applied by the wall on block B is

1. $80N$
2. $120N$
3. $150N$
4. $100N$

Q. Block A of mass $m$ and block $B$ of mass $2m$ are placed on a fixed tringular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure . The wedge is inclined at ${45}^{\circ }$ to the horizointal on both sides. If the coefficient of friction between the block $A$ and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

1. $1.2m/s^2$
2. $0.2m/s^2$
3. $-1m/s^2$
4. $\text{zero}$

Q. A block of mass $m$ rests on a rough horizontal surface as shown in the figure. Coefficient of friction between the block and the surface is $\mu$. A force $F=mg$ acting at angle $\theta$ with the vertical side of the block pulls it. In which of the following cases can the block be pulled along the surface?

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

Q. Consider a car moving on a straight road with a speed of $100m{s}^{-1}$. The distance at which car can be stopped is $[{\mu }_k=0.5]$

1. $800m$
2. $1000m$
3. $100m$
4. $400m$

Q.

The coefficients of static and kinetic friction between a body and the surface are 0.75 and 0.5 respectively. A force is applied to the body to make it just slide with a constant acceleration which is equal to

1. $\frac{g}{4}$

2. $\frac{g}{2}$

3. $\frac{3g}{4}$

4. $g$

Q. A block of mass $1\text{kg}$ is at rest on a horizontal table. The coefficient of static friction between the block and the table is $0.50$. If $g=10{\text{ms}}^{-2}$, then the magnitude of a force (in $\text{N}$) acting upwards at an angle of ${60}^{\circ }$ from the horizontal that will just start the block moving is

Q.

A boy pushes a box of mass, $2kg$ with a force, $F=20\overrightarrow{i}+10\overrightarrow{j}N$ on a frictionless surface. If the box was initially at rest, then what is displacement along the $x$-axis after $10s$?

Q.

A block of mass 2 kg is on a horizontal surface. The coefficient of static and kinetic friction are 0.6 and 0.2. The minimum horizontal force required to start the motion is applied and if it is continued, the velocity acquired by the body at the end of the 2nd second is?

Q. The maximum value of the block $m_2$ for which the system will remain in equilibrium (coefficient of friction between block $m_1$ and plane surface is $\mu$, pulleys are massless) is :

1. $\mu \frac{m_1}{2}$
2. $\frac{m_1}{2}$
3. $\mu m_1$
4. $2\mu m_1$

Q. The coefficient of static friction between the box and the train’s floor is 0.2. The maximum acceleration of the train upto which a box lying on its floor will remain stationary with respect to train is: (Take $g=10m{s}^{-2}$)

1. $8m{s}^{-2}$
2. $2m{s}^{-2}$
3. $4m{s}^{-2}$
4. $6m{s}^{-2}$

Q.

A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu ={\mu }_{0}x$, where $x$ is the distance through which the mass slides down, and ${\mu }_0$ a constant. Then, the speed is maximum after the mass covers a distance of

1. $\frac{\cos \theta }{{\mu }_0}$
2. $\frac{\sin \theta }{{\mu }_0}$
3. $\frac{\tan \theta }{{\mu }_0}$
4. $\frac{2\tan \theta }{{\mu }_0}$

Q.

A trolley of mass M is attached to a block of mass m by a string passing over a frictionless pulley as shown in the figure. If the coefficient of friction between the trolley and the surface below is $\mu ,$ what is the acceleration of the trolley and the block system when they are released?

1. $\left(\frac{m-M}{m+M}\right)g$

2. $\frac{m}{M}g$

3. $\left(\frac{\mu m-M}{m+M}\right)g$

4. $\left(\frac{m-\mu M}{m+M}\right)g$

Q. The retarding acceleration of $7.35{\text{ms}}^{-2}$ 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. $0.55$
2. $0.75$
3. $0.70$
4. $0.65$

Q. Block $A$ of weight $500\text{N}$ and block $B$ of weight $700\text{N}$ are connected by the rope pulley system, as shown in the figure. The largest weight $C$ that can be suspended without moving block $A$ and $B$ is $W$. The coefficient of friction for all plane surfaces of contact is $0.3$. The pulleys are ideal. The value of $\frac{W}{90}$ is ______.

Q.

Consider a uniform cubical box of side $a$ on a rough floor that is to be moved by applying minimum possible force $F$ at a point above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4$, the maximum value of $100\times \frac{b}{a}$ for the box not to topple before moving is $\_\_\_\_\_$.

Q. Three blocks $A,B$ and $C$ of mass $m$ each are arranged in pulley mass system as shown. Coefficient of friction between block $A$ and horizontal surface is equal to $0.5$ and a force $P$ acts on $‘A^{\prime }$ in the direction shown. The value of $\frac{P}{mg}$ so that block $‘C^{\prime }$ doesn’t move is

Q.

A block of mass m is placed on another block of mass M, which itself is lying on a horizontal surface. The coefficient of friction between two blocks is ${\mu }_1$ and that between the block of mass M and horizontal surface ${\mu }_2$. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?

1. $(M+m)({\mu }_2-{\mu }_1)g$

2. $(M+m)({\mu }_2-{\mu }_1)g$

3. $(M-m)({\mu }_2+{\mu }_1)g$

4. $(M+m)({\mu }_2+{\mu }_1)g$

Q.

An object of mass $2Kg$ is sliding with a constant velocity of $4\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ on a frictionless horizontal table. The force required to keep the object moving with the same velocity is

1. 32 N

2. 0 N

3. 2 N

4. 8 N

Q.

Two blocks of masses $m_1=4kg$ and $m_2=6kg$ are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure. The coefficient of friction between block $m_1$ and the horizontal surface is 0.4. When the system is released, the masses $m_{1}and{m}_2$ start accelerating. What additional mass $m$ should be placed over mass $m_1$ so that the masses $(m_1+m)$ slide with a uniform speed?

1. 9 kg

2. 10 kg

3. 11 kg

4. 12 kg

Q. Both the blocks are resting on a horizontal floor and the pulley is held such that the string remains just taut. At the moment $t=0$, a force $F=20t\text{N}$ starts acting on the pulley along vertically upward direction as shown in figure. Calculate the velocity of A as B loses contact with the floor.
[Take $g=10{\text{m/s}}^2$]

Q. A block of $7\text{kg}$ is placed on a rough horizontal surface and is pulled through a variable force F(in N) = 5t, where 't' is time in second, at an angle of ${37}^{\circ }$ with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at t = 0 s. Find the time (in sec.) at which the block starts to slide. (Take $g=10{\text{m/s}}^2)$:

Q. In an arrangement shown in the figure, the mass of $A=1\text{kg}$, the mass of $B=2\text{kg}$, and coefficient of friction between $A$ and $B$ is $0.2$. There is no friction between $B$ and the ground. The frictional force on $A$ is (Take $g=10{\text{m/s}}^2$)

(Assume there is no slipping between the blocks).

1. $\frac{5}{3}\text{N}$
2. $\frac{10}{3}\text{N}$
3. $2\text{N}$
4. $0\text{N}$

Q. A $30\text{kg}$ block rests on a rough horizontal surface. A horizontal force of $200\text{N}$ is applied on the body. The block acquires a speed of $4\text{m/sec}$, starting from rest, in $2\text{sec}$. What is the value of coefficient of friction?

1. $\frac{10}{\sqrt{3}}$
2. $\frac{\sqrt{3}}{10}$
3. $0.47$
4. $0.185$

Q. Block $B$ of mass $100\text{kg}$ rests on a rough surface of friction coefficient $\mu =\frac{1}{3}$. A rope is tied to block $B$ as shown in figure. The maximum acceleration with which boy $A$ of $25\text{kg}$ can climbs on rope without making block move is ($g=10m{s}^{-2}$)

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

Q. A car begins to move at time $t=0$ and then accelerates along a straight track with a velocity given by $V\left(t\right)=2t^2{\text{ms}}^{–1}$ for $0\le t\le 2$, where $t$ is time in second. After the end of acceleration, the car continues to move at a constant speed. A small block initially at rest on the floor of the car begins to slip at $t=1\text{s}$ and stops slipping at $t=3\text{s}$. The coefficient of static and kinetic friction between the block and the floor are ${\mu }_s$ and ${\mu }_k$ respectively. Find the value of $\frac{3{\mu }_s}{{\mu }_k}$ ($g=10m{s}^{-2}$)

Q. Two blocks of masses $5\text{kg}$ and $3\text{kg}$ are placed in contact over an inclined surface of angle ${37}^{\circ }$, as shown. ${\mu }_1$ is friction coefficient between $5\text{kg}$ block and the surface of the incline and similarly, ${\mu }_2$ is friction coefficient between the $3\text{kg}$ block and the surface of the incline. After the release of the blocks from the inclined surface, ($g=10{\text{m/s}}^2$)

1. if ${\mu }_1=0.5$ and ${\mu }_2=0.3$, then $5\text{kg}$ block exerts $3\text{N}$ force on the $3\text{kg}$ block
2. if ${\mu }_1=0.5$ and ${\mu }_2=0.3$, then $5\text{kg}$ block exerts $8\text{N}$ force on the $3\text{kg}$ block
3. if ${\mu }_1=0.3$ and ${\mu }_2=0.5$, then $5\text{kg}$ block exerts $1\text{N}$ force on the $3\text{kg}$ block
4. if ${\mu }_1=0.3$ and ${\mu }_2=0.5$, then $5\text{kg}$ block exerts no force on the $3\text{kg}$ block

Q. In the figure shown, the coefficient of static friction between $B$ and the wall is $\frac{2}{3}$ and the coefficient of kinetic friction between $B$ and the wall is $\frac{1}{3}$. Other contacts are smooth. If the minimum force ${}^{\prime }{F}^{\prime }$ required to lift $B$ up is $\frac{xmg}{2}$, then find $x$. Mass of $A$ is $2m$ and the mass of $B$ is $m$. Take $\tan \theta =\frac{3}{4}$.