Calculating Friction Using Coeffcients

Q. A plank of mass $2\text{kg}$ and length $9\text{m}$ is placed on a horizontal floor. A small block of mass $1\text{kg}$ is placed on top of the plank at its right extreme end. The coefficient of friction between the plank and the floor is $0.5$ and that between the plank and the block is $0.2$. If a horizontal force of $30\text{N}$ starts acting on the plank to the right, the time after which the block will fall off the plank is
(Take $g=10{\text{ms}}^{-2}$)

1. $2.96\text{s}$
2. $2\text{s}$
3. $1.75\text{s}$
4. $3.14\text{s}$

Q. A child of mass $30\text{kg}$ is sliding down a school slides with an angle of inclination of ${37}^{\circ }$ with horizontal. He can hold the railing on the sides of the slider in order to slide down without any acceleration. The force by the railing on the child for which he can do so is
(Given $\mu =\frac{1}{3}$ and $g=10{\text{m/s}}^2$)

1. $50\text{N}$ along $+x$ direction
2. $100\text{N}$ along $+x$ direction
3. $50\text{N}$ along $-x$ direction
4. $100\text{N}$ along $-x$ direction

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.

Two blocks A and B are connected to each other by a string and a spring of force constant k, as shown in the figure. The string passes over a frictionless pulley. Block B slides over the horizontal top surface of a stationary block C and block A slides along the vertical side of C both with the same uniform speed. If the coefficient of friction between the surfaces of the blocks is $\mu$ and the mass of block A is m, what is the mass of block B?

1. $\frac{m}{\sqrt{\mu }}$

2. $\frac{m}{\mu }$

3. $\sqrt{\mu m}$

4. $\mu m$

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. A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friciton 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 body of mass $2\text{kg}$ is kept on a rough horizontal surface. It is subjected to a force of a) $\text{5 N}$ b) $\text{20 N}$.
Given ${\mu }_s=0.5$ and ${\mu }_k=0.4$. Taking $g=10{\text{m/s}}^2$, find the acceleration in each case.

1. zero, zero
2. zero, $5{\text{m/s}}^2$
3. zero, $6{\text{m/s}}^2$
4. $4{\text{m/s}}^2,6{\text{m/s}}^2,$

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. The velocity-time graph in the figure given below shows the motion of a wooden block of mass $1\text{kg}$ which is given an initial push at $t=0$ along a horizontal table. Which of the following statements is/are correct ?

1. The coefficient of friction between the block and the table is $0.1$
2. The coefficient of friction between the block and the table is $0.2$
3. If the table has half of its present roughness, the time taken by the block to complete the journey is $4\text{s}$
4. If the table has half of its present roughness, the time taken by the block to complete the journey is $8\text{s}$

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. A body of mass $8\text{kg}$ lies on a rough horizontal table. It is observed that a certain horizontal force gives the body an acceleration of $4{\text{ms}}^{-2}$. When this force is doubled, the acceleration of the body is $16{\text{ms}}^{-2}$. The coefficient of friction is (take $g=10m{s}^{-2}$)

1. 0.2
2. 0.3
3. 0.4
4. 0.8

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 climb 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. 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 boy of mass m is sliding down a vertical pole by pressing it with a horizontal force $f$. If $\mu$ is the coefficient of friction between his palms and the pole, the acceleration with which he slides down will be equal to

1. $g$

2. $\frac{\mu f}{m}$

3. $g+\frac{\mu f}{m}$

4. $g-\frac{\mu f}{m}$

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 in covering the same distance, the coefficient of friction is

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

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 climb 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. 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 $\tan \theta =\frac{3}{4}$.

Q. A small body is projected with a velocity of $20.5{\text{ms}}^{-1}$ on a rough horizontal surface. The coefficient of friction $\left(\mu \right)$ between the surface changes with time ($t$ in $\text{s}$) as the body moves along the surface. The velocity at the end of $4\text{s}$ in ${\text{ms}}^{-1}$ will be

. (take $g=10{\text{ms}}^{-2}$)

Q.

A block of mass 0.1 kg is held against a wall applying a horizontal force of 5 N of the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is

1. 2.5 N

2. 0.98 N

3. 4.9 N

4. 0.49 N

Q.

The block $m_1$ is loaded on the block $m_2$. If there is no relative sliding between the blocks and the inclined plane is smooth, find the friction force between the blocks.

1. $m_{1}gsin\theta$

2. ($m_1+m_2$)g sin$\theta$

3. 0

4. $\mu m_{1}gcos\theta$

Q. A body of mass $8\text{kg}$ lies on a rough horizontal table. It is observed that a certain horizontal force gives the body an acceleration of $4{\text{ms}}^{-2}$. When this force is doubled, the acceleration of the body is $16{\text{ms}}^{-2}$. The coefficient of friction is (take $g=10m{s}^{-2}$)

1. 0.2
2. 0.3
3. 0.4
4. 0.8

Q. Find the ratio of tension $T_1$ and $T_2$ in the string as shown in figure if the whole system is moving with constant acceleration of $4m/s^2$ under the influence of force of magnitude $220N$ acting on block of mass $15kg$ . Assume the coefficient of friction to be $\mu =1/3$ and $g=10m/s^2$.

1. $0.35$
2. $0.45$
3. $0.2$
4. $5$

Q.

A boy of mass m is sliding down a vertical pole by pressing it with a horizontal force $f$. If $\mu$ is the coefficient of friction between his palms and the pole, the acceleration with which he slides down will be equal to

1. $g$

2. $\frac{\mu f}{m}$

3. $g+\frac{\mu f}{m}$

4. $g-\frac{\mu f}{m}$

Q. A block is placed on a rough horizontal plane. A time dependent horizontal force F = Kt acts on the block. Here, K is positive constant. Acceleration - time graph of the block is

1. 
2. 
3. 
4. 

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

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. Two blocks $m_1$ and $m_2$ are resting on a rough inclined plane of inclination ${37}^{\circ }$ as shown in figure. The contact force between the two blocks is
(Given $m_1=4\text{kg},m_2=2\text{kg},$ ${\mu }_1=0.8,{\mu }_2=0.5,g=10{\text{m/s}}^2,\sin {37}^{\circ }=3/5$)

1. $3.2\text{N}$
2. $3.6\text{N}$
3. $7.2\text{N}$
4. Zero

Q. A block of mass $10\text{kg}$ is moving with a uniform speed of $20\text{m/s}$ enters onto a rough surface of coefficient of friction $0.8$, the time taken by the block to come to rest is

1. $2.5\text{s}$
2. $5\text{s}$
3. $7.5\text{s}$
4. $10\text{s}$

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