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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

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## Solutions for Chapter 5: Newton's Laws of Motion

Below listed, you can find solutions for Chapter 5 of CBSE, Karnataka Board PUC HC Verma for Class 11, Class 12 Concepts of Physics Vol. 1.

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 5 Newton's Laws of Motion short answers [Pages 76 - 77]

The apparent weight of an object increases in an elevator while accelerating upward. A person sells peanuts using a beam balance in an elevator. Will he gain more if the elevator is accelerating up?

A boy puts a heavy box of mass M on his head and jumps from the top of a multi-storied building to the ground. What is the force exerted by the box on the boy's head during his free fall? Does the force greatly increase during the period he balances himself after striking the ground?

A person drops a coin. Describe the path of the coin as seen by the person if he is in (a) a car moving at constant velocity and (b) in a free falling elevator.

Is it possible for a particle to describe a curved path if no force acts on it? Does your answer depend on the frame of reference chosen to view the particle?

You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?

It is sometimes heard that the inertial frame of reference is only an ideal concept and no such inertial frame actually exists. Comment.

An object is placed far away from all the objects that can exert force on it. A frame of reference is constructed by taking the origin and axes fixed in this object. Will the frame be necessarily inertial?

The figure shows a light spring balance connected to two blocks of mass 20 kg each. The graduations in the balance measure the tension in the spring. (a) What is the reading of the balance? (b) Will the reading change if the balance is heavy, say 2.0 kg? (c) What will happen if the spring is light but the blocks have unequal masses?

The acceleration of a particle is zero, as measured from an inertial frame of reference. Can we conclude that no force acts on the particle?

Suppose you are running fast in a field and suddenly find a snake in front of you. You stop quickly. Which force is responsible for your deceleration?

If you jump barefoot on a hard surface, your legs are injured. But they are not injured if you jump on a soft surface like sand or pillow. Why?

According to Newton's third law, each team pulls the opposite team with equal force in a tug of war. Then, why does one team win and the other lose?

A spy jumps from an airplane with his parachute. The spy accelerates downward for some time when the parachute opens. The acceleration is suddenly checked and the spy slowly falls to the ground. Explain the action of the parachute in checking the acceleration.

Consider a book lying on a table. The weight of the book and the normal force by the table in the book are equal in magnitude and opposite in direction. Is this an example of Newton's third law?

Two blocks of unequal masses are tied by a spring. The blocks are pulled stretching the spring slightly and the system is released on a frictionless horizontal platform. Are the forces due to the spring on the two blocks equal and opposite? If yes, is it an example of Newton's third law?

When a train starts, the head of a standing passenger seems to be pushed backward. Analyse the situation from the ground frame. Does it really go backward? Coming back to the train frame, how do you explain the backward movement of the head on the basis of Newton's laws?

A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration 'a' along a straight horizontal track , the string supporting the bob makes an angle tan^{−1} (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan^{−1} (a/g), the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerating on a horizontal straight track or moving on an incline? If yes, how? If not, then suggest a method to do so.

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 5 Newton's Laws of Motion MCQ [Pages 77 - 78]

A body of weight w_{1} is suspended from the ceiling of a room by a chain of weight w_{2}. The ceiling pulls the chain by a force.

*w*_{1}w

_{2}*w*_{1}*+*w_{2}\[\frac{w_1 + w_2}{2}\]

When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by

the cart on the horse

the ground on the horse

the ground on the cart

the horse on the ground

A car accelerates on a horizontal road due to the force exerted by.

the engine of the car

the driver of the car

the earth

the road

A block of mass 10 kg is suspended from two light spring balances, as shown in the following figure.

Both the scales will read 10 kg.

Both the scales will read 5 kg.

The upper scale will read 10 kg and the lower zero.

The readings may be anything but their sums will be 10 kg.

A block of mass *m* is placed on a smooth inclined plane of inclination θ with the horizontal. The force exerted by the plane on the block has a magnitude.

mg

mg/cosθ

mg cosθ

mg tanθ

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude.

mg

mg/cosθ

mg cosθ

mg tanθ

Neglect the effect of rotation of the earth. Suppose the earth suddenly stops attracting objects placed near its surface. A person standing on the surface of the earth will.

fly up

slip along the surface

fly along a tangent to the earth's surface

remain standing

Three rigid rods are joined to form an equilateral triangle ABC of side 1 m. Three particles carrying charges 20 μC each are attached to the vertices of the triangle. The whole system is at rest in an inertial frame. The magnitude of the resultant force on the charged particle at A is.

zero

3.6 N

3.6`sqrt3` N

7.2 N

A force F_{1} acts on a particle accelerating it from rest to a velocity v. Force F_{1} is then replaced by F_{2} which decelerates the particle to rest.

F

_{1}must be equal to F_{2}.F

_{1}may be equal to F_{2}.F

_{1}must be unequal to F_{2}

Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.

The two bodies will reach the same height.

A will go higher than B.

B will go higher than A.

Any of the above three may happen depending on the speed with which the objects are thrown.

A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will.

take a time longer than T to slide down the wedge

take a time shorter than T to slide down the wedge

remain at the top of the wedge

jump off the wedge

In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle's motion. A particle of mass m projected upward takes time t_{1} in reaching the maximum height and t_{2} in the return journey to the original point. Then.

t

_{1}< t_{2}t

_{1}> t_{2}t

_{1}= t_{2}the relation between t

_{1}and t_{2}depends on the mass of the particle

A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator in time t_{1} if the elevator is stationary and in time t_{2} if it is moving uniformly. Then

t

_{1}= t_{2}t

_{1}< t_{2}t

_{1}> t_{2}t

_{1}< t_{2}or t_{1}> t_{2}depending on whether the lift is going up or down.

A free ** ^{238}U** nucleus kept in a train emits an alpha particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger, is

x + v t

x − v t

x

depends on the direction of the train

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 5 Newton's Laws of Motion MCQ [Pages 78 - 79]

A reference frame attached to the earth

(a) is an inertial frame by definition

(b) cannot be an inertial frame because the earth is revolving around the sun

(c) is an inertial frame because Newton's laws are applicable in this frame

(d) cannot be an inertial frame because the earth is rotating about its axis.

A particle stays at rest as seen in a frame. We can conclude that

(a) the frame is inertial

(b) resultant force on the particle is zero

(c) the frame may be inertial but the resultant force on the particle is zero

(d) the frame may be non-inertial but there is a non-zero resultant force

A particle is found to be at rest when seen from a frame S_{1} and moving with constant velocity when seen from another frame S_{2}. Mark out the possible options.

(a) Both the frames are inertial.

(b) Both the frames are non-inertial.

(c) S_{1} is inertial and S_{2} is non-inertial.

(d) S_{1} is non-inertial and S_{2} is inertial

The figure shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region

(a) AB

(b) BC

(c) CD

(d) DE

The figure shows a heavy block kept on a frictionless surface and being pulled by two ropes of equal mass m. At t = 0, the force on the left rope is withdrawn but the force on the right end continues to act. Let F_{1} and F_{2} be the magnitudes of the forces exerted by right rope and the left rope on the block, respectively.

F

_{1}_{ }= F_{2}= F for t < 0F

_{1}_{ }= F_{2}= F + mg for t < 0F

_{1}_{ }= F, F_{2}= F for t > 0F

_{1}< F, F_{2}= F for t > 0

The force exerted by the floor of an elevator on the foot of a person is more than the weight of the person if the elevator is

(a) going up and slowing down

(b) going up and speeding up

(c) going down and slowing down

(d) going down and speeding up

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be

(a) going up with increasing speed

(b) going down with increasing speed

(c) going up with uniform speed

(d) going down with uniform speed

A particle is observed from two frames S_{1} and S_{2}. Frame S_{2} moves with respect to S_{1}with an acceleration a. Let F_{1}_{ }and F_{2} be the pseudo forces on the particle when seen from S_{1} and S_{2}, respectively. Which of the following is not possible?

F

_{1}= 0, F_{2}≠ 0F

_{1}≠ 0, F_{2}= 0F

_{1}≠ 0, F_{2}≠ 0F

_{1}= 0, F_{2}= 0

A person says that he measured the acceleration of a particle to be non-zero even though no force was acting on the particle.

He is a liar.

His clock might have run slow.

His metre scale might have been longer than the standard.

He might have used a non-inertial frame.

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 5 Newton's Laws of Motion Exercise [Pages 79 - 83]

A block of mass 2 kg placed on a long frictionless horizontal table is pulled horizontally by a constant force F. It is found to move 10 m in the first seconds. Find the magnitude of F.

car moving at 40 km/hr is to be stopped by applying brakes in the next 4 m. If the car weighs 2000 kg, what average force must be applied to stop it?

In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 10^{6} m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10^{−31} kg.

A block of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the first block by another string. Find the tensions in the two strings. Take g = 10 m/s^{2}.

Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.

A particle of mass 50 g moves in a straight line. The variation of speed with time is shown in the following figure. Find the force acting on the particle at t = 2, 4 and 6 seconds.

Two blocks A and B of mass m_{A} and m_{B} , respectively, are kept in contact on a frictionless table. The experimenter pushes block A from behind, so that the blocks accelerate. If block A exerts force F on block B, what is the force exerted by the experimenter on block A?

Raindrops of radius 1 mm and mass 4 mg are falling with a speed of 30 m/s on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head.

A particle of mass 0.3 kg is subjected to a force F = −kx with k = 15 N/m. What will be its initial acceleration if it is released from a point x = 20 cm?

Both the springs shown in the following figure are unstretched. If the block is displaced by a distance *x* and released, what will be the initial acceleration?

A small block B is placed on another block A of mass 5 kg and length 20 cm. Initially, the block B is near the right end of block A (In the following Figure). A constant horizontal force of 10 N is applied to the block A. All the surfaces are assumed frictionless. Find the time that elapses before block B separates from A.

A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the following figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.

The elevator shown in the following figure is descending with an acceleration of 2 m/s^{2}. The mass of the block A is 0.5 kg. What force is exerted by the block A on the block B?

A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration 1.2 m/s^{2}, (b) goes up with deceleration 1.2 m/s^{2}, (c) goes up with uniform velocity, (d) goes down with acceleration 1.2 m/s^{2}, (e) goes down with deceleration 1.2 m/s^{2} and (f) goes down with uniform velocity.

A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg, respectively. Assuming that the magnitudes of acceleration and deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s^{2}.

Find the reading of the spring balance shown in the following figure. The elevator is going up with an acceleration g/10, the pulley and the string are light and the pulley is smooth.

A block of 2 kg is suspended from a ceiling by a massless spring of spring constant k = 100 N/m. What is the elongation of the spring? If another 1 kg is added to the block, what would be the further elongation?

Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of 2.0 m/s^{2}. Find the elongation.

The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?

An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?

A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?

In a simple Atwood machine, two unequal masses m_{1} and m_{2} are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the following figure), m_{1} = 300 g and m_{2} = 600 g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds; (b) find the tension in the string; (c) find the force exerted by the clamp on the pulley.

Consider the Atwood machine of the previous problem. The larger mass is stopped for a moment, 2.0 s after the system is set into motion. Find the time that elapses before the string is tight again.

In the following figure shows a uniform rod of length 30 cm and mass 3.0 kg. The strings shown in the figure are pulled by constant forces of 20 N and 32 N. Find the force exerted by the 20 cm part of the rod on the 10 cm part. All the surfaces are smooth and the strings and the pulleys are light.

Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.

A constant force F = m_{2}g/2 is applied on the block of mass m_{1} as shown in the following figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of m_{1}.

In the following figure, m_{1} = 5 kg, m_{2} = 2 kg and F = 1 N. Find the acceleration of either block. Describe the motion of m_{1} if the string breaks but F continues to act.

Let m_{1} = 1 kg, m_{2} = 2 kg and m_{3} = 3 kg in the following figure. Find the accelerations of m_{1}, m_{2} and m_{3}. The string from the upper pulley to m_{1} is 20 cm when the system is released from rest. How long will it take before m_{1} strikes the pulley?

In the previous problem, suppose *m*_{2} = 2.0 kg and *m*_{3} = 3.0 kg. What should be the mass *m*, so that it remains at rest?

Calculate the tension in the string shown in the following figure. The pulley and the string are light and all the surfaces are frictionless. Take g = 10 m/s^{2}.

Consider the situation shown in the following figure. Both the pulleys and the string are light and all the surfaces are frictionless. (a) Find the acceleration of the mass M; (b) find the tension in the string; (c) calculate the force exerted by the clamp on the pulley A in the figure.

Find the acceleration of the block of mass M in the situation shown in the following figure. All the surfaces are frictionless and the pulleys and the string are light.

Find the mass M of the hanging block in the following figure that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

Find the acceleration of the blocks A and B in the three situations shown in the following figure.

Find the acceleration of the 500 g block in the following figure.

A monkey of mass 15 kg is climbing a rope fixed to a ceiling. If it wishes to go up with an acceleration of 1 m/s^{2}, how much force should it apply on the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?

A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.

The monkey B, shown in the following figure, is holding on to the tail of monkey A that is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg, respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry monkey B with it? Take g = 10 m/s^{2}.

In the following figure shows a man of mass 60 kg standing on a light weighing machine kept in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling by a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight recorded on the machine? What force should he exert on the rope to record his correct weight on the machine?

A block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity v in the following figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.

A car is speeding up a horizontal road with acceleration *a*. Consider the following situations in the car: (i) A ball suspended from the ceiling by a string is maintaining a constant angle with the vertical. Find this angle. (ii) A block is kept on a smooth incline and does not slip on the incline. Find the angle of the incline with the horizontal.

A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s^{2}. Find the displacement of the block during the first 0.2 s after the start. Take *g* = 10 m/s^{2}.

## Solutions for Chapter 5: Newton's Laws of Motion

## HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 chapter 5 - Newton's Laws of Motion

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11, Class 12 Concepts of Physics Vol. 1 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. HC Verma solutions for Mathematics Class 11, Class 12 Concepts of Physics Vol. 1 CBSE, Karnataka Board PUC 5 (Newton's Laws of Motion) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. HC Verma textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Class 11, Class 12 Concepts of Physics Vol. 1 chapter 5 Newton's Laws of Motion are 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 and Its Characteristics, 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), Lubrication - (Laws of Motion), Law of Conservation of Linear Momentum and Its Applications, Rolling Friction, Introduction of Motion in One Dimension.

Using HC Verma Class 11, Class 12 Concepts of Physics Vol. 1 solutions Newton's Laws of Motion exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in HC Verma Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Class 11, Class 12 Concepts of Physics Vol. 1 students prefer HC Verma Textbook Solutions to score more in exams.

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