#### Chapters

Chapter 2: Physics and Mathematics

Chapter 3: Rest and Motion: Kinematics

Chapter 4: The Forces

Chapter 5: Newton's Laws of Motion

Chapter 6: Friction

Chapter 7: Circular Motion

Chapter 8: Work and Energy

Chapter 9: Centre of Mass, Linear Momentum, Collision

Chapter 10: Rotational Mechanics

Chapter 11: Gravitation

Chapter 12: Simple Harmonics Motion

Chapter 13: Fluid Mechanics

Chapter 14: Some Mechanical Properties of Matter

Chapter 15: Wave Motion and Waves on a String

Chapter 16: Sound Waves

Chapter 17: Light Waves

Chapter 18: Geometrical Optics

Chapter 19: Optical Instruments

Chapter 20: Dispersion and Spectra

Chapter 21: Speed of Light

Chapter 22: Photometry

#### H.C. Verma Concept of Physics Part-1 (2018-2019 Session) by H.C Verma

## Chapter 6: Friction

#### Chapter 6: Friction Exercise Short Answers solutions [Pages 95 - 96]

For most of the surfaces used in daily life, the friction coefficient is less than 1. Is it always necessary that the friction coefficient is less than 1?

Why is it easier to push a heavy block from behind than to press it on the top and push?

What is the average friction force when a person has a usual 1 km walk?

Why is it difficult to walk on solid ice?

Can you accelerate a car on a frictionless horizontal road by putting more petrol in the engine? Can you stop a car going on a frictionless horizontal road by applying brakes?

Spring fitted doors close by themselves when released. You want to keep the door open for a long time, say for an hour. If you put a half kg stone in front of the open door, it does not help. The stone slides with the door and the door gets closed. However, if you sandwitch a 20 g piece of wood in the small gap between the door and the floor, the door stays open. Explain why a much lighter piece of wood is able to keep the door open while the heavy stone fails.

A classroom demonstration of Newton's first law is as follows : A glass is covered with a plastic card and a coin is placed on the card. The card is given a quick strike and the coin falls in the glass. (a) Should the friction coefficient between the card and the coin be small or large? (b) Should the coin be light or heavy? (c) Why does the experiment fail if the card is gently pushed?

Can a tug of war be ever won on a frictionless surface?

Why do tyres have a better grip of the road while going on a level road than while going on an incline?

You are standing with your bag in your hands, on the ice in the middle of a pond. The ice is so slippery that it can offer no friction. How can you come out of the ice?

When two surfaces are polished, the friction coefficient between them decreases. But the friction coefficient increases and becomes very large if the surfaces are made highly smooth. Explain.

#### Chapter 6: Friction Exercise MCQ solutions [Page 96]

In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

increase

decrease

remain the same

may increase or decrease.

While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure

larger friction

smaller friction

larger normal force

smaller normal force.

A body of mass M is kept on a rough horizontal surface (friction coefficient = μ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on A is F, where

F = Mg

F = μ Mg

Mg ≤

Mg ≥

A scooter starting from rest moves with a constant acceleration for a time ∆t_{1}, then with a constant velocity for the next ∆t_{2} and finally with a constant deceleration for the next ∆t_{3} to come to rest. A 500 N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is

500 N throughout the journey

less than 500 N throughout the journey

more than 500 N throughout the journey

> 500 N for time ∆t

_{1}and ∆t_{3}and 500 N for ∆t_{2}_{.}

Consider the situation shown in figure. The wall smooth but the surface of A and B in contact are rough. The friction on B due to A in equilibrium

is upward

is downward

is zero

the system cannot remain in equilibrium.

Suppose all the surface in the previous problem are rough. The direction of friction of B due to A

is upward

is downward

is zero

depends on the masses of A and B

Two cars of unequal masses use similar tyres. If they are moving at the same initial speed, the minimum stopping distance

is smaller for the heavier car

is smaller for the lighter car

is same for both cars

depends on the volume of the car

In order to stop a car in shortest distance on a horizontal road, one should

apply the brakes very hard so that the wheels stop rotating

apply the brakes hard enough to just prevent slipping

pump the brakes (press and release)

shut the engine off and not apply brakes

A block A kept on an inclined surface just begins to slide if the inclination is 30°. The block is replaced by another block B and it is found that it just begins to slide if the inclination is 40°.

mass of A > mass of B

mass of A < mass of B

mass of A = mass of B

all of three are possible.

A boy of mass M is applying a horizontal force to slide a box of mass M' on a rough horizontal surface. The coefficient of friction between the shoes of the boy and the floor is μ and that between the box and the floor is μ'. In which of the following cases it is certainly not possible to slide the box?

μ < μ', M < M'

μ > μ', M < M'

μ < μ', M > M'

μ > μ', M > M'

#### Chapter 6: Friction Exercise MCQ solutions [Page 97]

Let F, F_{N} and f denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero.

(a) F > F_{N}

(b) F > f

(c) F_{N} > f

(d) F_{N} − f < F < F_{N} + f.

The contact force exerted by a body A on another body B is equal to the normal force between the bodies We conclude that

(a) the surface must be frictionless

(b) the force of friction between the bodies is zero

(c) the magnitude of normal force equal that of friction

(d) the bodies may be rough but they don't slip on each other.

Mark the correct statements about the friction between two bodies.

(a) Static friction is always greater than the kinetic friction.

(b) Coefficient of static friction is always greater than the coefficient of kinetic friction.

(c) Limiting friction is always greater than the kinetic friction.

(d) Limiting friction is never less than static friction.

A block is placed on a rough floor and a horizontal force F is applied on it. The force of friction f by the floor on the block is measured for different values of F and a graph is plotted between them.

(a) The graph is a straight line of slope 45°.

(b) The graph is a straight line parallel to the F-axis.

(c) The graph is a straight line of slope 45° for small F and a straight line parallel to the F-axis for large F.

(d) There is a small kink on the graph.

Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional force on the vehicle by the road

(a) is towards east if the vehicle is accelerating

(b) is zero if the vehicle is moving with a uniform velocity

(c) must be towards east

(d) must be towards west.

#### Chapter 6: Friction Exercise Exercise solutions [Pages 97 - 99]

A body slipping on a rough horizontal plane moves with a deceleration of 4.0 m/s^{2}. What is the coefficient of kinetic friction between the block and the plane?

A block is projected along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10, how far will it travel before coming to rest?

A block of mass m is kept on a horizontal table. If the static friction coefficient is μ, find the frictional force acting on the block.

A block slides down an inclined surface of inclination 30° with the horizontal. Starting from rest it covers 8 m in the first two seconds. Find the coefficient of kinetic friction between the two.

Suppose the block of the previous problem is pushed down the incline with a force of 4 N. How far will the block move in the first two seconds after starting from rest? The mass of the block is 4 kg.

A body of mass 2 kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the force parallel to the incline needed to make the block move (a) up the incline (b) down the incline. Coefficient of static friction = 0.2.

Repeat part (a) of problem 6 if the push is applied horizontally and not parallel to the incline.

In a children-park an inclined plane is constructed with an angle of incline 45° in the middle part (in the following figure). Find the acceleration of boy sliding on it if the friction coefficient between the cloth of the boy and the incline is 0.6 and *g* = 19 m/s^{2}.

A body starts slipping down an incline and moves half metre in half second. How long will it take to move the next half metre?

The angle between the resultant contact force and the normal force exerted by a body on the other is called the angle of friction. Show that, if λ be the angle of friction and μ the coefficient of static friction λ ≤ tan^{−1} μ.

Consider the situation shown in the following figure. Calculate (a) the acceleration of the 1.0 kg blocks, (b) the tension in the string connecting the 1.0 kg blocks and (c) the tension in the string attached to 0.50 kg.

If the tension in the string in the following figure is 16 N and the acceleration of each block is 0.5 m/s^{2}, find the friction coefficients at the two contact with the blocks.

The friction co-efficient between the table and the block shown in the following figure is 0.2. Find the tensions in the two strings.

The friction coefficient between a road and the type of a vehicle is 4/3. Find the maximum incline the road may have so that once had brakes are applied and the wheel starts skidding, the vehicle going down at a speed of 36 km/hr is stopped within 5 m.

The friction coefficient between an athelete's shoes and the ground is 0.90. Suppose a superman wears these shoes and races for 50 m. There is no upper limit on his capacity of running at high speeds. (a) Find the minimum time that he will have to take in completing the 50 m starting from rest. (b) Suppose he takes exactly this minimum time to complete the 50 m, what minimum time will he take to stop?

A care is going at a speed of 21.6 km/hr when it encounters at 12.8 m long slope of angle 30° (in the following figure). The friction coefficient between the road and the tyre is `1/2sqrt3`. 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 = 10 m/s^{2}.

A car starts from rest on a half kilometre long bridge. The coefficient of friction between the tyre and the road is 1.0. Show that one cannot drive through the bridge in less than 10 s.

In the following figure shows two blocks in contact sliding down an inclined surface of inclination 30°. The friction coefficient between the block of mass 2.0 kg and the incline is μ_{1}, and that between the block of mass 4.0 kg and incline is μ_{2}. Calculate the acceleration of the 2.0 kg block if (a) μ_{1} = 0.20 and μ_{2} = 0.30, (b) μ_{1} = 0.30 and μ_{2}_{ }= 0.20. Take g = 10 m/s^{2}.

Two masses M_{1} and M_{2} are connected by a light rod and the system is slipping down a rough incline of angle θ with the horizontal. The friction coefficient at both the contacts is μ. Find the acceleration of the system and the force by the rod on one of the blocks.

A block of mass M is kept on a rough horizontal surface. The coefficient of static friction between the block and the surface is μ. 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?

The friction coefficient between the board and the floor shown in the following figure is μ. Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.

A 2 kg block is placed over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the block is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to (a) the upper block, (b) the lower block. Take *g* = 10 m/s^{2}.

Find the accelerations a_{1}, a_{2}, a_{3} of the three blocks shown in the following figure if a horizontal force of 10 N is applied on (a) 2 kg block, (b) 3 kg block, (c) 7 kg block. Take g = 10 m/s^{2}.

The friction coefficient between the two blocks shown in the following figure is μ but the floor is smooth. (a) What maximum horizontal force F can be applied without disturbing the equilibrium of the system? (b) Suppose the horizontal force applied is double of that found in part (a). Find the accelerations of the two masses.

Suppose the entire system of the previous questions is kept inside an elevator which is coming down with an acceleration *a* < *g*. Repeat parts (a) and (b).

Consider the situation shown in the following figure. Suppose a small electric field E exists in the space in the vertically charge Q on its top surface. The friction coefficient between the two blocks is μ but the floor is smooth. What maximum horizontal force F can be applied without disturbing the equilibrium?

[**Hint**: The force on a charge Q bye the electric field E is F = QE in the direction of E.]

A block of mass m slips on a rough horizontal table under the action of a horizontal force applied to it. The coefficient of friction between the block and the table is μ. The table does not move on the floor. Find the total frictional force applied by the floor on the legs of the table. Do you need the friction coefficient between the table and the floor or the mass of the table?

Find the acceleration of the block of mass M in the situation of figure in the following. The coefficient of friction between the two blocks is μ_{1} and that between the bigger block and the ground is μ_{2}.

A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction? If no, find the frictional force exerted by the wall on the block.

A person (40 kg) is managing to be at rest between two vertical walls by pressing one wall A by his hands and feet and the other wall B by his back (in the following figure). Assume that the friction coefficient between his body and the walls is 0.8 and that limiting friction acts at all the contacts. (a) Show that the person pushes the two wall with equal force. (b) Find the normal force exerted by either wall on the person. Take *g* = 10 m/s^{2}.

In the following figure shows a small block of mass m kept at the left end of a larger block of mass M and length l. The system can slide on a horizontal road. The system is started towards right with an initial velocity v. The friction coefficient between the road and the bigger block is μ and that between the block is μ/2. Find the time elapsed before the smaller blocks separates from the bigger block.

## Chapter 6: Friction

#### H.C. Verma Concept of Physics Part-1 (2018-2019 Session) by H.C Verma

#### Textbook solutions for Class 12

## H.C. Verma solutions for Class 12 Physics chapter 6 - Friction

H.C. Verma solutions for Class 12 Physics chapter 6 (Friction) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Concept of Physics Part-1 (2018-2019 Session) by H.C Verma solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 12 Physics chapter 6 Friction are Lubrication - (Laws of Motion), Law of Conservation of Linear Momentum and Its Applications, Aristotle’s Fallacy, The Law of Inertia, Newton'S First Law of Motion, Newton’s Second Law of Motion, Newton's Third Law of Motion, Conservation of Momentum, Equilibrium of a Particle, Common Forces in Mechanics, Circular Motion, Solving Problems in Mechanics, Static and Kinetic Friction, Laws of Friction, Inertia, Intuitive Concept of Force, Dynamics of Uniform Circular Motion - Centripetal Force, Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road), Rolling Friction.

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