Study Material
LAWS OF MOTION
Very Short Answer Questions
Q1. Define absolute units of force in CGS as well as in SI System.
Q2. What is the law of inertia? Which scientist formulated it?
Q3. What do you understand by the term momentum?
Q4. Write units of momentum in (a) CGS system (b) SI System.
Q5. State the principle of conservation of linear momentum.
Q6. When a bullet is fired from a gun, the gun gives a kick in the backward direction. Explain.
Q7. Why cricketer pull back his hands, while catching the ball?
Q8. Why does a heavy rifle not recoil as strongly as a light rifle using the same cartridges?
Q9. If a bomb at rest explodes into two pieces, the pieces must travel in opposite directions. Explain.
Q10. Define force. What are the basic forces in nature?
Q12. What do you understand by the term Impulse and write its SI units.
Q13. Explain the following:
(a) why do we jerk wet clothes before spreading them on a rope?
(b) why does dust flyoff, when carpet is hit with a stick
(c) why do fruits fall off the branches in the strong wind
Q14. Can the coefficient of friction be greater than one? Give a reason.
Q15. What happens to the coefficient of friction if the weight of the body is doubled?
Q16. Why does the car with a flattened tyre stop sooner than the one with inflated tyres?
Q17. A horse has to pull harder during the start of the motion than later. Explain.
Q18. A bullet of mass \(0.05\,\mathrm{kg}\) moving with a speed of \(80\,\mathrm{m\,s^{-1}}\) enters a heavy wooden block and is stopped after a distance \(80\,\mathrm{cm}\). What is the average resistive force exerted by the block on the bullet?
Q19. A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \(10\,\mathrm{m\,s^{-1}}\). If the mass of the ball is \(0.25\,\mathrm{kg}\) determine the impulse imparted to the ball. (Assume linear motion of the ball.)
Q1. What do you understand by the term inertia? What are its kinds, Give two examples of each kind?
Q2. State Newton's three laws of motion? Give one example each to explain the first and third Laws.
Q3. State Newton's second law of motion. Hence derive the equation \(F=ma\) from it.
Q4. State Newton's three laws and discuss their Significance.
Q5. What do you understand by the following terms. Give the examples of each one?
(a) Contact forces
(b) Non-Contact forces.
Q6. Show that Impulse is the change of momentum.
Q7. Why are shock absorbers used in motor cycles and cars.
Q8. Define the terms momentum and impulse. State and explain the law of conservation of linear momentum. Give examples.
Q9. Explain the terms limiting friction, dynamic friction and rolling friction.
Q10. Explain advantages and disadvantages of friction.
Q11. Mention different methods used to decrease friction.
Q12. Under what condition will a car skid on a leveled circular road?
Q13. Briefly Explain centrifugal force with suitable examples.
Q14. Derive an expression for maximum velocity of a car moving in a circular motion on a level road.
Q15. Determine the maximum acceleration of the train in which a box lying on its floor will remain stationery, given that the co-efficient of static friction between the box and train's floor is \(0.18\).
Q1. Derive an expression for maximum velocity of a car moving in circular motion on a banked road.
Q1. A body has a linear momentum of \(5\,\mathrm{N\,s}\). If the velocity of the body is \(200\,\mathrm{m\,s^{-1}}\), find the mass of the body?
Q2. Calculate the velocity of a body of mass \(0.5\,\mathrm{kg}\), when it has a linear momentum of \(5\,\mathrm{N\,s}\).
Q3. A motorcycle of mass \(100\,\mathrm{kg}\) is running at \(10\,\mathrm{m\,s^{-1}}\). Its engine develops an extra linear momentum of \(2000\,\mathrm{N\,s}\). Calculate the new velocity of motorcycle.
Q4. A Force \(F_1\), acting on a \(2.0\,\mathrm{kg}\) body produces an acceleration of \(2.5\,\mathrm{m\,s^{-2}}\). Another Force \(F_2\) acting on a \(5\,\mathrm{kg}\) body produces an acceleration of \(2\,\mathrm{m\,s^{-2}}\), find the ratio \(F_2/F_1\).
Q5. A Force of \(10\,\mathrm{N}\) towards the east and unknown force \(F\) balance each other. Find the unknown force.
Q6. A Force produces an acceleration of \(5\,\mathrm{cm\,s^{-2}}\) when it acts on a body of mass \(20\,\mathrm{g}\). Find the force in newtons.
Q7. A force of \(12\,\mathrm{N}\) starts acting on a body kept at rest, find the momentum of the body at \(1\,\mathrm{s}\), \(2\,\mathrm{s}\) and \(5\,\mathrm{s}\) after the force starts acting.
Q8. The linear momentum of a particle as a function of time \(t\) is given by \(p=a+bt\), where \(a\) and \(b\) are positive constants. What is the force acting on the particle?
Q9. Calculate the time needed for a net force of \(5\,\mathrm{N}\) to change the velocity of \(10\,\mathrm{kg}\) mass by \(2\,\mathrm{m\,s^{-1}}\).
Q10. A ball of mass \(m\) is thrown vertically upward from the ground and reaches a height \(h\) before momentarily coming to rest. If \(g\) is acceleration due to gravity. What is the impulse received by the ball due to gravity force during its flight? (neglect air resistance)
Q11. A constant force acting on a body of mass \(3.0\,\mathrm{kg}\) changes its speed from \(2.0\,\mathrm{m\,s^{-1}}\) to \(3.5\,\mathrm{m\,s^{-1}}\) in \(2.5\,\mathrm{s}\). The direction of motion of the body remains unchanged. What is the magnitude and direction of the force?
Q12. A man in a lift feels an apparent weight \(W\) when the lift is moving up with a uniform acceleration of \(1/3\) of the acceleration due to gravity. If the same man were in the same lift now moving down with a uniform acceleration that is \(1/2\) of the acceleration due to gravity, then what is his apparent weight?
Q13. A container of mass \(200\,\mathrm{kg}\) rests on the back of an open truck. If the truck accelerates at \(1.5\,\mathrm{m\,s^{-2}}\), what is the minimum coefficient of static friction between the container and the bed of the truck required to prevent the container from sliding off the back of the truck?
Q14. A bomb initially at rest at a height of \(40\,\mathrm{m}\) above the ground suddenly explodes in to two identical fragments. One of them starts moving vertically downwards with an initial speed of \(10\,\mathrm{m\,s^{-1}}\). If acceleration due to gravity is \(10\,\mathrm{m\,s^{-2}}\), What is the separation between the fragments \(2\,\mathrm{s}\) after the explosion?
Q15. A fixed pulley with a smooth groove has a light string passing over it with a \(4\,\mathrm{kg}\) attached on one side and a \(3\,\mathrm{kg}\) on the other side. Another \(3\,\mathrm{kg}\) is hung from the other \(3\,\mathrm{kg}\) as shown with another light string. If the system is released from rest, find the common acceleration? (\(g=10\,\mathrm{m\,s^{-2}}\))
Q16. A block of mass \(2\,\mathrm{kg}\) slides on an inclined plane that makes an angle of \(30^\circ\) with the horizontal. The coefficient of friction between the block and the surface is \(\sqrt{3}/2\).\n(a) What force should be applied to the block so that it moves down without any acceleration?\n(b) What force should be applied to the block so that it moves up without any acceleration?
Q17. A block is placed on a ramp of parabolic shape given by the equation \(y=x^2/20\), see Fig. If \(\mu_s=0.5\), what is the maximum height above the ground at which the block can be placed without slipping?
Q18. A block of metal of mass \(2\,\mathrm{kg}\) on a horizontal table is attached to a mass of \(0.45\,\mathrm{kg}\) by a light string passing over a frictionless pulley at the edge of the table. The block is subjected to a horizontal force by allowing the \(0.45\,\mathrm{kg}\) mass to fall. The coefficient of sliding friction between the block and table is \(0.2\). Calculate (a) the initial acceleration, (b) the tension in the string, (c) the distance the block would continue to move if, after \(2\,\mathrm{s}\) of motion, the string should break.
Q19. On a smooth horizontal surface a block \(A\) of mass \(10\,\mathrm{kg}\) is kept. On this block a second block \(B\) of mass \(5\,\mathrm{kg}\) is kept. The coefficient of friction between the two blocks is \(0.4\). A horizontal force of \(30\,\mathrm{N}\) is applied on the lower block as shown. What is the force of friction between the blocks? (take \(g=10\,\mathrm{m\,s^{-2}}\))
Q1. A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \(12\,\mathrm{m\,s^{-1}}\). If the mass of the ball is \(0.15\,\mathrm{kg}\), determine the impulse imparted to the ball. (Assume linear motion of the ball.)
Q2. 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?
Q3. See Fig. 4.8. A mass of \(6\,\mathrm{g}\) is suspended by a rope from the ceiling. A horizontal force of \(50\,\mathrm{N}\) is applied at the mid-point of the rope, as shown. What is the angle the rope makes with the vertical when in equilibrium? (Take \(g=10\,\mathrm{m\,s^{-2}}\). Neglect the mass of the rope.)
Q4. Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and train's floor is \(0.15\).
Q5. See Fig. 4.11. A mass of \(4\,\mathrm{kg}\) rests on a rough incline. The plane is gradually inclined until the angle is at \(\theta=15^\circ\) with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?
Q6. What is the acceleration of the block and trolley shown in Fig. 4.12(a), if the coefficient of kinetic friction between the trolley and the surface is \(0.04\)? What is the tension in the string? (Take \(g=10\,\mathrm{m\,s^{-2}}\). Neglect the mass of the string.)
Q7. A cyclist speeding at \(18\,\mathrm{km\,h^{-1}}\) on a level road takes a sharp circular turn of radius \(3\,\mathrm{m}\) without reducing the speed. The coefficient of static friction between the tyres and the road is \(0.1\). Will the cyclist slip?
Q8. A circular racetrack of radius \(300\,\mathrm{m}\) is banked at an angle of \(15^\circ\). If the coefficient of friction between the wheels of a race-car and the road is \(0.2\), what is the (a) optimum speed of the race-car to avoid wear and tear of its tyres, and (b) maximum permissible speed to avoid slipping?
Q9. See Fig. 4.15. A wooden block of mass \(2\,\mathrm{kg}\) rests on a soft cylinder of mass \(25\,\mathrm{kg}\) placed on top of the block. The floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1\,\mathrm{m\,s^{-2}}\). What is the action on the block on the floor (a) before and (b) after the floor yields? Take \(g=10\,\mathrm{m\,s^{-2}}\). Identify the action-reaction pairs in the problem.
Q10. An astronaut accidentally gets separated out of his small spaceship accelerating in inter stellar space at a constant rate of \(100\,\mathrm{m\,s^{-1}}\). What is the acceleration of the astronaut at the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him.)
Q11. A bullet of mass \(0.08\,\mathrm{kg}\) moving with a speed of \(90\,\mathrm{m\,s^{-1}}\) enters a heavy wooden block and is stopped after a distance of \(1.5\,\mathrm{m}\). What is the average resistive force exerted by the block on the bullet?
Q12. The motion of a particle of mass \(m\) is described by \(y=ut+\frac{1}{2}gt^2\). Find the force acting on the particle.