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Physics · Textbook solutions

Laws of Motion

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 35 questions

Worked Examples

12 q

Solved Examples

Worked · 12
  1. Eg 4.1
    An astronaut accidentally gets separated out of his small spaceship accelerating in inter stellar space at a constant rate of 100 m s−2100\,\text{m s}^{-2}. What is the acceleration of the astronaut the instant after he is outside the spaceship ? (Assume that there are no nearby stars to exert gravitational force on him.)
  2. Eg 4.2
    A bullet of mass 0.04 kg0.04\,\text{kg} moving with a speed of 90 m s−190\,\text{m s}^{-1} enters a heavy wooden block and is stopped after a distance of 60 cm60\,\text{cm}. What is the average resistive force exerted by the block on the bullet?
  3. Eg 4.3
    The motion of a particle of mass mm is described by y=ut+12gt2y = ut + \dfrac{1}{2}gt^2. Find the force acting on the particle.
  4. Eg 4.4
    A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m s−112\,\text{m s}^{-1}. If the mass of the ball is 0.15 kg0.15\,\text{kg}, determine the impulse imparted to the ball. (Assume linear motion of the ball)
  5. Eg 4.5
    Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Fig. 4.6. What is (i) the direction of the force on the wall due to each ball? (ii) the ratio of the magnitudes of impulses imparted to the balls by the wall ?
  6. Eg 4.6
    See Fig. 4.8. A mass of 6 kg6\,\text{kg} is suspended by a rope of length 2 m2\,\text{m} from the ceiling. A force of 50 N50\,\text{N} in the horizontal direction is applied at the mid-point P of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take g=10 m s−2g = 10\,\text{m s}^{-2}). Neglect the mass of the rope.
  7. Eg 4.7
    Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the co-efficient of static friction between the box and the train's floor is 0.150.15.
  8. Eg 4.8
    See Fig. 4.11. A mass of 4 kg4\,\text{kg} rests on a horizontal plane. The plane is gradually inclined until at an angle θ=15∘\theta = 15^\circ with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface ?
  9. Eg 4.9
    What is the acceleration of the block and trolley system shown in a Fig. 4.12(a), if the coefficient of kinetic friction between the trolley and the surface is 0.040.04? What is the tension in the string? (Take g=10 m s−2g = 10\,\text{m s}^{-2}). Neglect the mass of the string.
  10. Eg 4.10
    A cyclist speeding at 18 km/h18\,\text{km/h} on a level road takes a sharp circular turn of radius 3 m3\,\text{m} without reducing the speed. The co-efficient of static friction between the tyres and the road is 0.10.1. Will the cyclist slip while taking the turn?
  11. Eg 4.11
    A circular racetrack of radius 300 m300\,\text{m} is banked at an angle of 15∘15^\circ. If the coefficient of friction between the wheels of a race-car and the road is 0.20.2, what is the (a) optimum speed of the race-car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping ?
  12. Eg 4.12
    See Fig. 4.15. A wooden block of mass 2 kg2\,\text{kg} rests on a soft horizontal floor. When an iron cylinder of mass 25 kg25\,\text{kg} is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of 0.1 m s−20.1\,\text{m s}^{-2}. What is the action of the block on the floor (a) before and (b) after the floor yields ? Take g=10 m s−2g = 10\,\text{m s}^{-2}. Identify the action-reaction pairs in the problem.

Exercises

23 q
  1. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.1
    Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed, (b) a cork of mass 10 g10\,\text{g} floating on water, (c) a kite skillfully held stationary in the sky, (d) a car moving with a constant velocity of 30 km/h30\,\text{km/h} on a rough road, (e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
  2. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.2
    A pebble of mass 0.05 kg0.05\,\text{kg} is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during its upward motion, (b) during its downward motion, (c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45∘45^\circ with the horizontal direction? Ignore air resistance.
  3. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.3
    Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg0.1\,\text{kg}, (a) just after it is dropped from the window of a stationary train, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h36\,\text{km/h}, (c) just after it is dropped from the window of a train accelerating with 1 m s−21\,\text{m s}^{-2}, (d) lying on the floor of a train which is accelerating with 1 m s−21\,\text{m s}^{-2}, the stone being at rest relative to the train. Neglect air resistance throughout.
  4. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.4
    One end of a string of length ll is connected to a particle of mass mm and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed vv the net force on the particle (directed towards the centre) is : TT is the tension in the string. [Choose the correct alternative].
    1. A.
      TT
    2. B.
      T−mv2lT - \dfrac{mv^2}{l}
    3. C.
      T+mv2lT + \dfrac{mv^2}{l}
    4. D.
      00
  5. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.5
    A constant retarding force of 50 N50\,\text{N} is applied to a body of mass 20 kg20\,\text{kg} moving initially with a speed of 15 m s−115\,\text{m s}^{-1}. How long does the body take to stop ?
  6. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.6
    A constant force acting on a body of mass 3.0 kg3.0\,\text{kg} changes its speed from 2.0 m s−12.0\,\text{m s}^{-1} to 3.5 m s−13.5\,\text{m s}^{-1} in 25 s25\,\text{s}. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
  7. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.7
    A body of mass 5 kg5\,\text{kg} is acted upon by two perpendicular forces 8 N8\,\text{N} and 6 N6\,\text{N}. Give the magnitude and direction of the acceleration of the body.
  8. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.8
    The driver of a three-wheeler moving with a speed of 36 km/h36\,\text{km/h} sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s4.0\,\text{s} just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg400\,\text{kg} and the mass of the driver is 65 kg65\,\text{kg}.
  9. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.9
    A rocket with a lift-off mass 20,000 kg20{,}000\,\text{kg} is blasted upwards with an initial acceleration of 5.0 m s−25.0\,\text{m s}^{-2}. Calculate the initial thrust (force) of the blast.
  10. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.10
    A body of mass 0.40 kg0.40\,\text{kg} moving initially with a constant speed of 10 m s−110\,\text{m s}^{-1} to the north is subject to a constant force of 8.0 N8.0\,\text{N} directed towards the south for 30 s30\,\text{s}. Take the instant the force is applied to be t=0t = 0, the position of the body at that time to be x=0x = 0, and predict its position at t=−5 st = -5\,\text{s}, 25 s25\,\text{s}, 100 s100\,\text{s}.
  11. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.11
    A truck starts from rest and accelerates uniformly at 2.0 m s−22.0\,\text{m s}^{-2}. At t=10 st = 10\,\text{s}, a stone is dropped by a person standing on the top of the truck (6 m6\,\text{m} high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t=11 st = 11\,\text{s} ? (Neglect air resistance.)
  12. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.12
    A bob of mass 0.1 kg0.1\,\text{kg} hung from the ceiling of a room by a string 2 m2\,\text{m} long is set into oscillation. The speed of the bob at its mean position is 1 m s−11\,\text{m s}^{-1}. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.
  13. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.13
    A man of mass 70 kg70\,\text{kg} stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of 10 m s−110\,\text{m s}^{-1}, (b) downwards with a uniform acceleration of 5 m s−25\,\text{m s}^{-2}, (c) upwards with a uniform acceleration of 5 m s−25\,\text{m s}^{-2}. What would be the readings on the scale in each case? (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
  14. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.14
    Figure 4.16 shows the position-time graph of a particle of mass 4 kg4\,\text{kg}. What is the (a) force on the particle for t<0t < 0, t>4 st > 4\,\text{s}, 0<t<4 s0 < t < 4\,\text{s}? (b) impulse at t=0t = 0 and t=4 st = 4\,\text{s} ? (Consider one-dimensional motion only).
  15. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.15
    Two bodies of masses 10 kg10\,\text{kg} and 20 kg20\,\text{kg} respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F=600 NF = 600\,\text{N} is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?
  16. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.16
    Two masses 8 kg8\,\text{kg} and 12 kg12\,\text{kg} are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
  17. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.17
    A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
  18. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.18
    Two billiard balls each of mass 0.05 kg0.05\,\text{kg} moving in opposite directions with speed 6 m s−16\,\text{m s}^{-1} collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
  19. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.19
    A shell of mass 0.020 kg0.020\,\text{kg} is fired by a gun of mass 100 kg100\,\text{kg}. If the muzzle speed of the shell is 80 m s−180\,\text{m s}^{-1}, what is the recoil speed of the gun ?
  20. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.20
    A batsman deflects a ball by an angle of 45∘45^\circ without changing its initial speed which is equal to 54 km/h54\,\text{km/h}. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg0.15\,\text{kg}.)
  21. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.21
    A stone of mass 0.25 kg0.25\,\text{kg} tied to the end of a string is whirled round in a circle of radius 1.5 m1.5\,\text{m} with a speed of 40 rev./min40\,\text{rev./min} in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N200\,\text{N} ?
  22. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.22
    If, in Exercise 4.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks : (a) the stone moves radially outwards, (b) the stone flies off tangentially from the instant the string breaks, (c) the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?
  23. (For simplicity in numerical calculations, take g=10 m s−2g = 10\,\text{m s}^{-2})
    Ex 4.23
    Explain why (a) a horse cannot pull a cart and run in empty space, (b) passengers are thrown forward from their seats when a speeding bus stops suddenly, (c) it is easier to pull a lawn mower than to push it, (d) a cricketer moves his hands backwards while holding a catch.