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CHAPTER : FIVE, , LAWS OF MOTION, , ARISTOTLE’S FALLACY:, An external force is required to keep a body in motion., Explanation: According to Aristotle, if a body is moving, something external is required to, keep it moving., Example: An arrow shot from a bow keeps flying since the air behind the arrow keeps pushing it., THE LAW OF INERTIA:, The law of inertia was inferred/given by Galileo., If the net external force is zero, a body at rest continues to remain at rest and a body in, motion continues to move with a uniform velocity. This property of the body is called, inertia. Inertia means „resistance to change’., A body does not change its state of rest or of uniform motion unless an external force, compels it to change that state., Illustrations (Examples) for inertia:, 1. A person sitting in a vehicle at rest has his whole body at rest. When the vehicle suddenly, starts moving forward the lower part of the body in contact with the vehicle moves, forward. But the upper part of the body continues to remain at rest due to inertia. As a, result the person has a tendency to fall back., 2. The dust particles in the carpet fall off when beaten with a stick. Beating sets the carpet, into motion while the dust particles tend to remain at rest due to inertia and hence gets, separated from the carpet., 3. In a moving bus, the body of a person has same velocity as that of the bus. When the bus, suddenly comes to rest, the lower part of the body in contact with bus comes to rest. But, the upper part of the body continues to move forward due to inertia. As a result the person, falls forward., 4. When a knife is sharpened by pressing it against grinding stone, the sparks fly off, tangential to the grinding stone. The reason is the sparks are hot specks of metal detached, from the knife. They move tangentially due to inertia of direction., MASS: The quantity of matter present in a body is called its mass. Inertia of a body is, directly proportional to mass. i.e., more the mass, more is the opposition offered by the body, to change its state., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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NEWTON’S FIRST LAW OF MOTION:, Statement: “Every body continues to be in its state of rest or of uniform motion in a, straight line unless compelled by some external force to act otherwise”., Explanation: According to this law, if there is no external force, a body at rest continues to, be at rest and a body in motion continues to move with same velocity. If the net external, force on the object is zero then we can say that the acceleration of the object is zero., Example: A spaceship out in interstellar space, far from all other objects and with all its, rockets turned off, has no net external force acting on it. Its acceleration, according to the, first law, must be zero. If it is in motion, it must continue to move with a uniform velocity., MOMENTUM (p):, , , , , , , , , , Momentum p of a body is defined to be the product of its mass m and velocity v . p = m v ., Momentum of a body is the quantity of motion present in the body., Momentum of a body can also be defined as the capacity of the body to give motion, (velocity) to another body., , , ,  Momentum is a vector quantity and its direction is along v .,  S.I. unit of momentum is kg m s–1 or Ns.,  Dimensional formula of momentum is [M1L1T–1] or simply [MLT–1]., Illustrations: Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle, (say a loaded truck) are parked on a horizontal road. We all know that a much greater force, is needed to push the truck than the car to bring them to the same speed in same time., Similarly, a greater opposing force is needed to stop a heavy body than a light body in the, same time, if they are moving with the same speed., • If two stones, one light and the other heavy, are dropped from the top of a building, a, person on the ground will find it easier to catch the light stone than the heavy stone. The, mass of a body is determines the effect of force on its motion., • Speed is another quantity to consider in momentum. A bullet fired by a gun can easily, pierce human tissue before it stops, resulting in casualty. The same bullet fired with, moderate speed will not cause much damage. Thus for a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time. Taken together,, the product of mass and velocity, that is momentum, is evidently a relevant variable of, motion. The greater the change in the momentum in a given time, the greater is the force that, needs to be applied.,  The same force for the same time causes the same change in momentum for, different bodies., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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NEWTON’S SECOND LAW OF MOTION:, Statement: “The rate of change of momentum of a body is directly proportional to the, applied force and takes place in the direction in which the force acts”., , , , Derivation of F  m a, , , , If under the action of a force F for time interval Δt, the velocity of a body of mass m changes, , , , , , , , from v to v   v, , , , , , , , ,  , , i.e., its initial momentum p  m v changes by p  m  v, , , ,  Δp, , Δp, or F  k, According to the II Law: F , ; where k is the constant of proportionality., Δt, Δt, , Δp, Taking the limit t  0, the term, becomes the derivative or differential co-efficient of, Δt, , , , , , d, p, dp, p with respect to t, is, . Thus F = k, dt, dt, , , , , , dp, d, dv, =, m, v, =, m, , m, a, For a body of fixed mass m,, dt, dt, dt, ,  , , , , , ,  dv,  a, dt, , i.e., the second law can also be written as F = k m a, , , , It shows that, the force is proportional to the product of mass m and acceleration a ., ,  dp, ,  ma, Let F=1, m=1, a=1 then we get k=1. The second law then is F=, dt, , SI unit force is newton: 1 N = 1 kg m s–2., Definition of one newton: One newton is that force which causes an acceleration of 1 m s–2, to a mass of 1 kg., IMPULSE:, Suppose a large force acts for a very short duration producing a finite change in momentum, of the body. Here the force and the time duration are difficult to measure separately., However, the product of force and time, which is the change in momentum of the body,, remains a measurable quantity. This product is called impulse., For example, when a ball hits a wall and bounces back, the force on the ball by the wall acts, for a very short time when the two are in contact, but the force is large enough to reverse the, momentum of the ball., Impulse of a force: The product of the force and the time is called impulse of a force., Impulse = Force × time duration = Change in momentum, Large force acting for a short time to produce a finite change in momentum is called as, impulsive force., E.g.: Hammering a nail in to a wall, hitting a ball by a bat., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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Prove that impulse of a force is equal to change in momentum:, Consider a force F acting on a body of mass m for a time interval t., Let v0 and v be the initial and final velocities., Impulse of a force = force  time = (m a)  t, =m, ,  v  v0 , t, , × t = m v – m v0 = change in momentum., , Thus impulse of a force is measured by the change in momentum produced in the body., SI unit of impulse is newton second (Ns) or kg ms–1., Dimensional formula of impulse of a force [M L T–1]., NEWTON’S THIRD LAW OF MOTION:, Statement: “To every action, there is always an equal and opposite reaction”, Explanation: Action means the force exerted by the first body on the second. Reaction, means the force exerted by the second body on the first. Action and reaction, are equal and, opposite, do not cancel because they act on two different bodies., E.g.:,  While walking, a person presses the ground backwards (action) by his feet. The, ground pushes the person forward with equal force (reaction).,  When a bullet is fired from a gun, the bullet is pushed forward by the gun (action) and, the gun recoils (reaction).,  A swimmer pushes water backwards (action) and in turn water pushes him forward, (reaction).,  Consider a wooden block placed on the surface of a table. The block exerts a force, equal to its weight W on the table. The surface of the table in turn exerts a reaction, force R on the block. If W be the action force then R is the reaction force. They are, equal in magnitude but opposite in direction.,  When a tennis ball is thrown against a wall, the ball bounces back due to the reaction, of the wall.,  When a person jumps out of a boat, the boat is pushed in the opposite direction due to, the reaction force., , I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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CONSERVATION OF LINEAR MOMENTUM:, Statement:, The total momentum of an isolated system of interacting particles is conserved., Proof:, , , , Consider two bodies A and B, with initial momenta p A and p B respectively., , , , , The bodies collide and get apart, with final momenta p'A and p'B respectively., ,  , ,  , From Newton‟s Second Law: FAB (Δt)  p'A  pA, and FBA (Δt)  p'B  pB, , (Where we, , have taken a common interval of time for both forces i.e., the time for which the two bodies, are in contact), , , , , , Since FAB  FBA by the Newton‟s III law,, , , , FAB (Δt)  FBA (Δt),  ,  , p'A  pA  (p'B  pB ),    , p'A  p'B  pA  pB, , That is, the total final momentum of the isolated system is equal to total initial momentum., , Illustrations:, 1. Bullet and gun: Before firing, the bullet of mass „m‟ and the gun of mass „M‟ are at rest., Total initial momentum = 0., , , , , After firing, bullet moves forward with a velocity v and the gun recoils with a velocity V ., According to law of conservation of momentum,, Total initial momentum = Total final momentum., , , , i.e., 0 = m v + M V, , , , mv,  Recoil velocity: V  , M, , The negative sign indicates that the recoiling velocity of the gun is opposite in direction to, the velocity of the outgoing bullet., 2. Rocket propulsion: A rocket is used to launch satellites to a suitable height above the, ground. The fuel in the rocket is burnt and the exhaust gases escape downwards at high, speed. Rocket moves upwards due to the reaction force. As rocket moves up,,  Its mass gradually decreases.,  The total momentum of rocket and the burnt fuel is conserved., , I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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EQUILIBRIUM OF A PARTICLE:, Equilibrium of a particle in mechanics means, the net external force on the particle is zero., According to Newton‟s first law, this means that,, the particle is either at rest or in uniform motion., , , , , , , , , If two forces F1 and F2 act on a particle, equilibrium requires that F1 =  F2, i.e., the two forces on the particle must be equal (in magnitude) and opposite (in direction)., , , , , , , Equilibrium under three concurrent forces F1 , F2 and F3 requires that the vector sum of the,    , three forces is zero. i.e., F1  F2  F3  0, , , , , In other words, the resultant of any two forces say F1 and F2 , obtained by the parallelogram, , , law of forces must be equal and opposite to the third force F3 ., CONTACT FORCES:, A contact force on an object arises due to contact with some other object, solid or fluid. The, component of contact force normal to the surface in contact is called normal reaction. The, component parallel to the surface in contact is called friction. Buoyant force, viscous force,, air resistance are the examples of contact force., Basic forces in nature: In order of increasing strength, the various forces in nature are, 1. Gravitational force:, It is the force of attraction between any two objects by virtue of their masses., 2. Weak nuclear force:, It is the force that exists in certain nuclear interactions such as −decay., 3. Electromagnetic forces: It is the force between the charged particles., 4. Strong nuclear force: It is the force existing between the nucleons (protons & neutrons), in a nucleus., Other common forces are tension in a string, the force due to spring etc., Tension (T): Consider a wire with one end fixed to a support. When a load is suspended, from the other end, restoring forces are set up in the wire due to elasticity. This restoring, force in the wire is called the tension and is denoted by T., Spring force : When a spring is compressed or stretched due to an external force, a restoring, force is set up in the spring. This restoring force brings the spring back to its initial state, when the external force is removed. This restoring force is called the spring force. The, spring force is directly proportional to the displacement from the initial state., i.e., F  x where x is displacement., Thus F  k x , where k is the proportionality constant called “spring constant” or “spring, modulus” or “force constant” . Negative sign indicates that the displacement and force are, oppositely directed., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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FRICTION:, Friction is that force which opposes the relative motion between two surfaces in contact., Friction is the opposing force that comes into play when one body actually or tries to move, over the surface of another., Origin of friction: Friction arises due to the roughness of the surfaces and molecular forces, of attraction at the points of actual contacts. On account of the roughness of the surfaces, the, area of actual contact is much smaller than area of apparent contact. Area of actual contact, depends on the force with which the two surfaces are “pressing” against each other i.e. it, depends on the normal force on the surface. For an object on a horizontal surface, the force, on the surface is equal to the normal reaction that is equal to the weight of the body on the, surface. Due to this force, the molecules at the point of actual contact come very close and, they exert strong attractive forces on one another. Thus, to that extent the surfaces stick, together. The temporary molecular bonds formed have to be broken to make the surfaces, slide. This is the force which prevents the relative movement between the surfaces and, causes friction., TYPES OF FRICTION:, , fsmax, , STATIC FRICTION:, It is the force of friction, which exactly balances the, , fk, F= fs, f, , applied external force (F) when the body is in equilibrium, (rest) and is denoted by fs., Static fiction is self-adjusting force:, , 450, F, , When there is no applied force, there is no static friction. It comes, when the moment there is an applied force. As the applied force F, increases, fs also increases, remaining equal and opposite to the, applied force (up to a certain limit), keeping the body at rest., Hence, it is called static friction., Static friction opposes impending motion. The impending motion means motion that would, take place (but does not actually take place) under the applied force, if friction were absent., When the applied force F is gradually increased, fs also increases and attains a maximum, value (fs)max. As the applied force exceeds a certain limit, the body begins to move., This value is called limiting static friction. At this limiting value, the body is about to move, in the direction of the applied force. Once the motion sets in, the frictional force decreases., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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LAW OF STATIC FRICTION:, Force of static friction: fs ≤ μs N; the constant μs is called the coefficient of static friction.,  The force of limiting friction between two given surfaces is always opposite to the, direction of applied force or the direction in which the motion tends to take place.,  The force of limiting friction acts tangentially to the two surfaces in contact.,  The magnitude of the limiting friction is directly proportional to the normal reaction, between the two surfaces.,  The magnitude of the limiting friction is independent of the shape or area of the surfaces, in contact provided the normal reaction remains the same.,  The limiting friction depends upon the material and the nature of the surfaces and their, smoothness., KINETIC FRICTION:,  Frictional force that opposes relative motion between surfaces in, contact is called kinetic or sliding friction., , , Kinetic friction is independent of the area of contact., , , , Kinetic friction is nearly independent of the velocity., , , , The kinetic friction is the frictional force, which comes into play when the two, bodies in contact are in relative motion., , , , Kinetic friction which comes into play when a solid body slides over the surface of, another is called sliding friction., , LAW OF KINETIC FRICTION:, Force of kinetic friction: fk = μk N; the constant μk is called the coefficient of kinetic friction.,  μk is less than μs.,  When relative motion between two bodies begins, the acceleration of the body :, a=, , Net force F  f k, , mass, m, ,  For a body moving with constant velocity (as a = 0), F = fk .,  If the applied force (F) on the body is removed (F=0), acceleration a= – fk/m and it, eventually comes to a stop.,  As θ increases, the self-adjusting frictional force fs, increases until at θ = θmax , fs = μsN block starts, siding and θmax = tan–1 (μs), ANGLE OF FRICTION ():, The angle made by the resultant of the force of limiting friction fsmax and the normal reaction, N, with the normal reaction is called angle of friction., If s denotes coefficient of static friction, then  = tan–1 (s)., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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ROLLING FRICTION:, , , Kinetic friction which comes into play when a solid, body rolls over the surface of another solid is called, rolling friction., , , , A body like a ring or a sphere rolling without slipping over a horizontal plane will, suffer no friction., , , , Example: Ball bearings placed between moving parts of a machine as shown in the, adjacent figure reduces the kinetic friction due to rolling., , ADVANTAGES OF FRICTION:,  Without friction we cannot walk.,  Without friction vehicles cannot move on the road and cannot be stopped by applying brakes., ,  Without friction one cannot hold anything in one‟s hand., DISADVANTAGES OF FRICTION:,  Friction causes power dissipation in the form of heat, sound etc.,  Friction causes wear and tear of the parts of a machine and reduces their life time.,  Frictional forces result in the production of heat which can be harmful to the, machinery parts.,  Efficiency of a machine is reduced, as extra energy is required to overcome the friction., METHODS OF REDUCING FRICTION: Friction can be reduced, , , By lubrication with oil, Greece, powder etc., , , , By using ball bearings (as rolling friction is less than kinetic friction)., , , , By polishing and making the surface smoother., , , , By proper selection of materials which offer low friction., , , , By streamlining i.e., suitable shaping of objects moving in air or liquid., , CENTRIPETAL FORCE (fc): The force directed towards the centre along the radius, during circular motion of an object is called the centripetal force., EXPRESSION FOR CENTRIPETAL FORCE:, fc = mv2/R ; m-mass, v- speed of the body and R - radius of circular path., Examples: 1) For a stone rotated in a circle by a string, the centripetal force is provided by, the tension in the string., 2) The centripetal force for motion of a planet around the sun is the gravitational force on, the planet due to the sun., 3) For a car taking a circular turn on a horizontal road, the centripetal force is the force of friction., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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MOTION OF A CAR ON A LEVEL ROAD:, Let a car of mass m moving on a circular level road of, radius R with a speed v., Three forces act on the car:, (i) The weight of the car (W= mg), vertically downwards., (ii) Normal reaction (N), vertically upwards., (iii) Frictional force (f), towards the centre of a circular path along radius acting horizontally., As there is no acceleration in the vertical direction, N – mg = 0, , N = mg, , The static friction provides the necessary centripetal acceleration (force) for the car to, move in circular path, , f  μs N =, , mv2,  mv2  μs R N, R, ,  N = m g, , m v2  μs R m g, , v2  μs R g ,, , which is independent of the mass of the car., , Thus, for a given value of μs and R, the maximum speed of circular motion of the car, , vmax = μs g R, MOTION OF A CAR ON A BANKED ROAD:, Let a car of mass m moving on a circular banked road of, radius R with a speed v. Let the angle of banking be θ., (i) The weight of the car (W= mg), vertically downwards., (ii) Normal reaction (N)., (iii) Frictional force (f), acting along the banked road., The Normal reaction (N) is resolved in to two components,, vertically upwards – N cosθ and horizontal component – N sinθ, The frictional force (f) is resolved in to two components,, vertically downwards – f sinθ & horizontal component – f cosθ., Since there is no acceleration along the vertical direction, the net, force along vertical direction must be zero., Net upward force = Net downward force, N cosθ = mg + f sinθ, , ………………. (1), , The centripetal force is provided by the horizontal components of N and f., , I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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QUESTION BANK:, ONE MARK/TWO MARKS QUESTIONS:, 1. What is Aristotle’s fallacy (State Aristotelian law of motion)?,  An external force is required to keep the body in motion., 2. Is Aristotelian law correct? Justify you answer., 3. Why uniformly moving body comes to rest?,  Due to opposing force /frictional force., 4. What is uniform motion?,  If a body covers equal distance in equal intervals of time, however small the interval may be., , 5. Who discovered Aristotelian law of motion?,  Galileo Galilei, 6. What is inertia? Who gave this concept?, 7. What is the measure of inertia?,  Gravitational mass., 8. Give an example for inertia of rest., 9. Give an example for inertia of motion., 10. State Newton’s first law of motion., 11. State the law of inertia., 12. What is the acceleration of a body having uniform linear motion?, 13. What is the force on a body moving with uniform speed?, 14. Whose ideas did Newton make use of while framing his famous laws of motion?, 15. A space ship out in an interstellar space, far from all other objects and with all its, rockets turned off, has zero acceleration but still in motion, Why?, 16. Define linear momentum of a body., 17. Is linear momentum of a body is scalar or a vector?, 18. Write the S.I unit of linear momentum., 19. Write the dimensional formula for linear momentum., 20. Why do athletes run a few steps before taking a jump?, 21. Why a passenger standing in a bus fall backwards, when the bus suddenly starts moving?, 22. Why a passenger getting down from a moving bus must run a few steps in the, direction of the motion of the bus?, 23. Why is it more difficult to catch a cricket ball than a tennis ball thrown with same velocity?, 24. Why a cricketer does lower his hand soon after/while catching a cricket ball?, I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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25. Give an example for an object having magnitude of momentum fixed but change in direction., 26. Define impulse of a force. What is an impulsive force? Give an example., 27. Write the SI unit and dimensional formula of impulse., 28. State and explain Newton’s third law of motion with an example., 29. State the law of conservation of linear momentum., 30. What is meant by equilibrium of a particle?, 31. What is friction? Define frictional force., 32. What is meant by static friction?, 33. What is meant by normal reaction force?, 34. What is meant by the limiting force of friction?, 35. Define co-efficient of static friction., 36. What is kinetic (sliding) friction?, 37. What is rolling friction?, 38. Mention any two advantages of friction and any two disadvantages of friction., 39. Give any two methods of reducing friction., 40. Write the SI unit and dimensional formula for force., 41. Define 1 newton, the SI unit of force.,  A force acting on a body is said to be 1 newton if accelerates the body of mass 1 kg by 1 ms–2., , 42. State and explain Newton’s third law of motion with example., 43. What is the change in momentum of a particle in uniform circular motion at, diametrically opposite points?, 44. Mention the common forces in mechanics., 45. Write the expression for the spring force and explain the terms., 46. In mechanics we come across so many contact forces, their origin is electrical force, though the particles are neutral. Explain., 3 and 5 MARKS QUESTIONS:, 1. State Newton’s second law of motion and hence derive 𝐅 = 𝐦 𝐚., 2. State and prove the principle of law of conservation of linear momentum., 3. What is centripetal force? Give the expression for it and explain the terms., 4. Write the steps to be followed to solve problems in mechanics., 5. Derive the expression for maximum speed of circular motion of a car on (i) a level road, (ii) on a banked road., I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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2 and 5 MARKS NUMERICAL PROBLEMS:, 1. A block of mass 500 g is at rest on a horizontal table. What steady force is required to, give a stationary block a velocity of 200 cm s–1 in 4 s ?, [Ans.: Force F = ma = m(v–u)/t = 0.5(2–0)/4 = 0.25 N], 2. What is the force acting on a body of mass 50 g if it accelerates the body by 3 ms–2 ?, [Ans.: Force: F = ma = (0.05)(3) = 0.15 N], 3. A net external force of 5 N is acting on a body of mass 10 kg. What is the acceleration, [Ans.: Acceleration a = F/m = 10/5 = 2 ms–2 ], , produced?, , 4. Compare the linear momenta of two bodies one of mass 100 g moving with a speed of, 50 ms–1 and another body of mass 0.5 kg moving with a speed of 25 cm s–1., [Ans.:, , p1, mv, 0.1 50, 5,  11 =, ,  40 ], p2 m2 v 2 0.5  0.25 0.125, , 5. The time rate of change of momentum of a body is 5 kg ms–2. What is the force acting, on the body?, , [Ans.: 5N], , 6. A 50 g bullet is fired from a 10 kg gun with a speed of 500 ms–1. What is the speed of, the recoil of the gun?, , [Ans.: 2.5 m/s], , 7. 20 J work is required to stretch a spring through 0.1 m. Find the force constant of the, spring., , [Ans.: 4000 N/m], , 8. A force acts for 20 second on a body of mass 10 kg (which was initially at rest), after, which the force ceases and the body describes 50 m in the next 10 seconds., Find the magnitude of the force., , [Ans.: F = 2.5 N], , 9. A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Find the, magnitude and direction of the acceleration., [Ans.: a = F/m=10/5 =2m/s2 makes an angle tan-1(3/4) with 8 N], 10. A constant retarding force of 50 N is applied to a body of mass 10 kg moving initially, with a speed of 15 m/s. How long the body does takes to stop?, [Ans.: a = F/m=50/10 =5m/s2 , t = 3s], 11. A force 10 N acts on a body for 3  10–6 s. Calculate the impulse. If the mass of the, body is 5 g, calculate the change in velocity., 12. A circular race track of radius 300 m is banked at an angle of 15°. If the coefficient of, friction between the wheels of a race car and the road is 0.2,, What is (i) The optimum speed of the race car to avoid wear and tear of the tyres and, (ii) Maximum permissible speed to avoid slipping?, I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075

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13. A stone of mass 250 gram tied to the end of a string is whirled in a circle of radius, 1.5 m, with a speed of 40 revolutions per minute in horizontal plane., (a) What is the tension in the string?, (b) Calculate the maximum speed with which a stone can be whirled, if the string, can withstand a maximum tension of 200 N., 14. A block of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an, angle 150 with the horizontal, the block just begins to slide. Find the coefficient of, static friction between the block and the surface., 15. A monkey of mass 40 kg climbs on a rope which can stand a maximum tension 500 N., In which of the following cases will the rope break?, (Take g = 10 m/s2 and ignore the mass of the rope), The monkey (a) climbs up with an acceleration of 5 m/s2., (b) climbs down with an acceleration of 2 m/s2., (c) climbs up with a uniform speed of 10 m/s., (d) falls down the rope freely under gravity., *Ans.: (a) Tension T= Apparent weight W’ =m(g+a) = 40(10+5)= 600N is more than maximum, tension that the rope can withstand, thus the rope breaks., (b) Tension T= Apparent weight W’ =m(g – a) = 40(10 – 2) = 320 N is less than maximum, tension, rope doesn’t break., (c) Tension T= Apparent weight W’ =m(g – a) = 40(10 – 0) = 400 N is less than maximum, tension, rope doesn’t break., (d) Tension T= Apparent weight W’ = m(g – a) = 40(10 – 10) = 0 , rope doesn’t break+, 16. A man weighs 60 kg. He stands on a weighing machine in a lift, which is moving, (Take g = 10 m/s2), (a) Upwards with a uniform speed of 6 m/s., (b) Downward with a uniform acceleration of 6 m/s2., (c) Upwards with a uniform acceleration of 6 m/s2., (i) What would be the reading of the scale in each case?, (ii) What would be the reading if the lift mechanism fails, and fall freely?, [Ans.: (i) (a) 600N (b) 240N (c) 960 N, , (ii) 0], , I PUC PHYSICS : SHREENIVASA M BHAT, GPUC, KARWAR : 9740541938, 9964073075