Finding Friction's Magnitude

Q.

A block of mass M is kept on a rough horizontal surface. The coefficient of static friction between the block and the surface is $\mu .$ the block is to be pulled by applying a force to it. what minimum force is needed to slide the block ? In which direction should this force act?

Q. A system of two blocks of masses $m=2kg$ and $M=8kg$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $\mathrm{0.5.}$ The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be

1. $9.8N$
2. $39.2N$
3. $49N$
4. $78.4N$

Q. A block of mass $3\text{kg}$ is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be $(g=10{\text{m/s}}^2)$

1. $26\text{N}$
2. $19.5\text{N}$
3. $10\text{N}$
4. $30\text{N}$

Q. If three particles, each of mass $M$, are placed at the three corners of an equilateral triangle of side $a$, the forces exerted by this system on another particle of mass $M$ placed
$\left(i\right)$ at the midpoint of a side and
$\left(ii\right)$ at the centre of the triangle are respectively,

1. $0,\frac{4G{M}^2}{3a^2}$
2. $\frac{4G{M}^2}{3a^2},0$
3. $\frac{3G{M}^2}{a^2},\frac{G{M}^2}{a^2}$
4. $0,0$

Q.

A block of weight 200 N is pulled along a rough horizontal surface at a constant speed by a force of 100 N acting at an angle of ${30}^{\circ }$ above the horizontal. The coefficient of friction between the block and the surface is

1. 0.58

2. 0.43

3. 0.75

4. 0.85

Q. A ball is placed on a smooth inclined plane of inclination $\theta ={30}^{\circ }$ to the horizontal, the inclined plane is rotating at frequency $0.5$ $\text{Hz}$ about a vertical axis passing through its lower end. At what distance from the lower end does the ball remains at rest?

1. $0.87\text{m}$
2. $0.33\text{m}$
3. $0.5\text{m}$
4. $0.67\text{m}$

Q.

A body takes time ‘t’ to reach the bottom of an inclined plane of angle $\theta$ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is:

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

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

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

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

Q. For the arrangement shown in the figure, the tension in the string is given by $(sin{37}^{\circ }=\frac{3}{5})$. Take $g=10m{s}^{-2}$

1. $40N$
   
2. $60N$
3. $30N$
4. $30N$

Q. A force $F=(\hat{i}+4\hat{j})\text{N}$ acts on the block shown. The force of friction acting on the block is :

1. $-\hat{i}\text{N}$
2. $-18\hat{i}\text{N}$
3. $-2.4\hat{i}\text{N}$
4. $-3\hat{i}\text{N}$

Q. A uniform ladder of length $5\text{m}$ and mass $100\text{kg}$ is in equilibrium between a vertical smooth wall and a rough horizontal surface as shown below. Find the minimum friction co-efficient between floor and ladder for this equilibrium.

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

Q.

Two blocks 'A' and 'B' each of mass 'm' are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks 'A' and 'B' respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is: (Assume no friction between blocks)

1. F

2. 3F

3. 4F

4. 2F

Q. A block is gently placed on a conveyor belt moving horizontally at a constant speed. After $t=4\text{s}$, the velocity of the block becomes equal to the velocity of the belt. If the coefficient of static friction between the block and the belt is $\mu =0.2$, then what is the velocity of the conveyor belt ?

1. $2\text{m/s}$
2. $4\text{m/s}$
3. $6\text{m/s}$
4. $8\text{m/s}$

Q.

A block released from rest from the top of a smooth inclined plane of inclination ${45}^{\circ }$ takes $t$ seconds to reach the bottom. The same block released from rest from the top of a rough inclined plane of the same inclination of ${45}^{\circ }$ takes $2t$ seconds to reach the bottom. The coefficient of friction is

1. $\sqrt{0.75}$

2. $\sqrt{0.5}$

3. $0.5$

4. $0.75$

Q. A block placed on a rough inclined plane of inclination $(\theta ={30}^{\circ })$ can just be pushed upwards by applying a force ${}^{\prime }{F}^{\prime }$ as shown. If the angle of inclination of the inclined plane is increased to $(\theta ={60}^{\circ })$, the same block can just be prevented from sliding down by the application of a force of the same magnitude. The coefficient of friction between the block and the inclined plane is

1. $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
2. $\frac{2\sqrt{3}-1}{\sqrt{3}+1}$
3. $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
4. None of these

Q.

The minimum velocity in ($m{s}^{-1}$) with which a car driver must traverse a flat curve of radius $150m$ and coefficient of friction $0.6$ to avoid skidding is ?

1. $60m{s}^{-1}$

2. $30m{s}^{-1}$

3. $15m{s}^{-1}$

4. $25m{s}^{-1}$

Q.

A block of mass 5 kg is lying on a rough horizontal surface. The coefficients of static and kinetic friction between the block and the surface respectively are 0.7 and 0.5. A horizontal force just sufficient to move the block is applied to it. If the force continues to act even after the block has started moving, what will be the acceleration of the block? Take $g=10m{s}^{-2}$.

1. $1m{s}^{-2}$

2. $2m{s}^{-2}$

3. $3m{s}^{-2}$

4. $4m{s}^{-2}$

Q. Block $\text{A}$ is placed on a rough wedge $\text{B}$ which is placed on a smooth surface. The wedge has angle of inclination of ${30}^{\circ }$ and is imparted a horizontal acceleration $g$ towards right. Block $\text{A}$ is given an initial velocity $v_0$ from rest. Find the coefficient of friction for which block $\text{A}$ moves with constant velocity $v_0$ with respect to wedge $(g=10{\text{m/s}}^2)$

1. $\frac{(3+\sqrt{3})}{(3-\sqrt{3})}$
   
2. $\frac{(2-\sqrt{3})}{(2+\sqrt{2})}$
3. $\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}$
   
4. $\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}$

Q. Wedge is fixed on a horizontal surface. Triangular block A of mass $M$ is pulled upward by applying a constant force $F$ parallel to the incline of the wedge as shown in the figure and there is no friction between the wedge and the block A, while coefficient of friction between A and block B of mass $m$ is $\mu .$ If there is no relative motion between A and B, then frictional force developed between A and B is

1. $\left[\frac{F+(m-M)gsin\theta }{m+M}\right]mcos\theta$
2. $\mu mg$
3. $\frac{\mu mg}{2}$
4. $\left[\frac{F-(m+M)gsin\theta }{m+M}\right]mcos\theta$

Q.

A $5.0kg$ crate is on an incline that makes an angle of ${30}^{°}$ with the horizontal. If the coefficient of static friction is $0.5$, the maximum force that can be applied parallel to the plane without moving the plane to hold the crate at rest is

1. Zero

2. $3.3N$

3. $30N$

4. $46N$

Q. A block of mass $m$ rests on a horizontal table with coefficient of static friction $\mu$. What minimum force must be applied on the block to drag it on the table?

1. $\frac{\mu }{\sqrt{1+{\mu }^2}}mg$
2. $\frac{\mu }{\sqrt{1-{\mu }^2}}mg$
3. $\frac{\mu -1}{\mu +1}mg$
4. $\mu mg$

Q.

A car is going at a speed of 21.6 km/hr when it encounters a 12.8 m long slope of angle ${30}^{\circ }$ (figure 6-E5).
The friction coefficient between the road and the tyre is \frac{1}{2\sqrt{3}}. Show that no matter how hard the driver applies the brakes, the car will reach the bottom with a speed greater than 36 km/hr. Take g = $10m/s^2$

Q.

A conveyor belt is moving at a constant speed of $2m/s$, a box is gently dropped on it. The coefficient of friction between them is $0.5$. The distance that the box will move relative to the belt before coming to rest on it (taking $g=10m/s^2$), is

Q.

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and $g=10m{s}^{-2}$, the horizontal force that he is applying on the pole is

1. 300 N

2. 400 N

3. 500 N

4. 600 N

Q.

A fixed ring of mass m has two beads A, B of mass m each; both being able to slide on the ring without friction. Initially the ring lies on a frictionless horizontal table and the beads are given velocities ${\nu }_0$ , relative to the ring, in the same direction. The initial relative acceleration of one of the beads with respect to the other is

1. $zero$
2. $\frac{v_0^2}{R}$
3. $\frac{2v_0^2}{R}$
4. $\frac{v_0^2}{2R}$

Q. A block of mass $15\text{kg}$ is acted upon by a force $25\text{N}$ at an angle ${37}^{\circ }$ with the horizontal in a direction as shown in figure. The coefficient of static friction($\mu$) between the block and horizontal surface is $0.2$ . Find the frictional force acting on the block, so that it doesn't move. Take $(g=10{\text{m/s}}^2)$.

1. $33\text{N}$
2. $13\text{N}$
3. $10\text{N}$
4. $20\text{N}$

Q. Two blocks $A$ and $B$ weighing $2\text{kg}$ and $8\text{kg}$ respectively are tied with an inextensible string. The coefficient of kinetic and static friction between the blocks and the horizontal surface is $0.25$ and $0.3$ respectively. If horizontal force $F=25\text{N}$, then find the acceleration of block $A$ and $B$.

1. $2.5{\text{m/s}}^2$
2. $2{\text{m/s}}^2$
3. $\text{Zero}$
4. $4{\text{m/s}}^2$

Q. Two blocks $A$ of 6 $kg$ and $B$ of 4 $kg$ are placed in contact with each other as shown in figure.

There is no friction between $A$ and ground and between both the blocks. The coefficient of friction between $B$ and ground is 0.5. A horizontal force $F$ is applied on $A$. Find the minimum and maximum values of $F$, which can be applied so that both the blocks can move combinely without any relative motion between them.

1. 10 $N$, 50 $N$
2. 12 $N$, 50 $N$
3. 12 $N$, 75 $N$
4. None of these

Q. Figure shows a pair of pin jointed gripper tongs holding an object weighing $2000\text{N}$. The coefficient of friction $\mu$ at the gripping surface is $0.1$. $X-X^{\prime }$ is the line of action of the input force and $Y-Y^{\prime }$ is the line of application of normal gripping force. If the pin-joint is assumed as frictionless, the magnitude of force $F$ required to hold the weight (in $\text{N}$) is

Q. A block moving with initial velocity $u=20\text{m/s}$ comes to rest after covering distance of $40m$ on a rough plane. Find out coefficient of kinetic friction. (Take $g=10m/s^2$)

1. $0.5$
2. $0.25$
3. $0.75$
4. Data incomplete

Q.

A body is moving down a long inclined plane of angle of inclination $\theta$. The coefficient of friction between the body and the plane varies as $\mu =0.5x$, where $x$is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by

1. $x=2tan\theta$

2. $x=\frac{2}{tan\theta }$

3. $x=\sqrt{2}cot\theta$

4. $x=\frac{\sqrt{2}}{cot\theta }$