# Assignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE

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1 Assignment Work (Physics) Class :Xi Chapter :04: Motion In PLANE State law of parallelogram of vector addition and derive expression for resultant of two vectors i.e,. What do you mean by trajectory? Also define the term projectile motion. What is meant by the range of the projectile and what will be the effect on the horizontal range of a projectile when its initial speed doubled keeping its angle of projection same. What do you mean by a projectile? Show that the path followed by a projectile thrown horizontally with a uniform velocity from the top of a tower is parabolic. Also obtain an expression for (i) maximum height, (ii) time of flight and (iii) horizontal range. Show that the path followed by a projectile is a parabolic, when it is projected at an angle the horizontal and also find expressions for (i) maximum height attained (ii) total time of flight and (iii) horizontal range. Deduce the expression for (i) maximum height, (ii) time of flight and (iii) horizontal range for inclined projection. What do you mean by relative velocity. Explain it with the help of diagram and example. Define scalar product with two example and also write its property. Define vector product with two example and explain its applications. A particle starts moving from the origin of x y plane and is at a point (3,2) after 2s. Calculate the displacement of the particle after 2s. Draw the velocity time graphs for two particle in one dimensional motion when their relative acceleration is (i) zero, and (ii) non zero. A river is flowing due east with a speed 3 m/s. A swimmer can swim in still water at a speed of 4 m/s. (a) If with swimmer starts swimming due north, what will be his resultant velocity. (b) If he wants to

2 start from point A on south bank and reach opposite point B on north bank; (i) Which direction should he swims? (ii) what will be his resultant speed? 13. A stone is thrown with a horizontal velocity of 15 m/s from the top of the tower. If the stone hits the ground at a distance of 100 m from the foot of the tower, calculate the height of the top. 14. Calculate the angle of projection of the projectile if the horizontal range is equal to the maximum height attained. 15. A projectile of mass 50 g is fired with velocity 10 m/s at an angle of 30 0 with the horizontal. Calculate (i) the linear momentum and (ii) kinetic energy of projectile at highest point. 16. Prove that a gun will shoot a bullet three times as high when its angle of elevation is 60 0 as when it is 30 0 but will cover the same horizontal distance. 17. A bullet is fired from a fifle attains a maximum height of 25 m and crosses a range of 200 m. find the angle of projection. 18. A stone is thrown upward from a point on the side of a hill with a speed of 30 m/s at an angle of 60 0 with the horizontal. If the hill slopes upward uniformly at an angle of 20 0, then at what distance up the slope does the ball hit and after what time.

3 Assignment Work (Physics) Class :Xi Chapter :05: LAWS OF MOTION(NEWTON S LAW OF MOTION) 1. Action and reaction are equal and opposite. Why cannot they cancel each other? 2. Why a gun recoils back when it is being fired? 3. A body is acted upon by a number of external forces. Can it remain at rest? 4. The rate of change of momentum of a body is 2 kg m/s. What is force acting on the body? 5. Why does a heavy gun not recoil so strongly as a light gun firing the same bullet? 6. No force is required to move a body with constant velocity. Explain. 7. A bullet fired from a gun is more dangerous than an air molecule hitting a person, though both of them have almost the same speed. Explain. 8. Newton s first law of motion is the law of inertia. Explain. 9. What is inertia? Define and explain the three different types of inertia. 10. State Newton s second law of motion. How does it help to measure force? Also show that Newton s second law of motion is the only real law of motion. 11. State Newton s second law of motion. Hence derive the equation of motion F = ma. 12. Discuss the motion of horse- cart problem. 13. Explain the term impulse. Show that the impulse is equal to the change in momentum. 14. Discuss graphical method for the measurement of impulse in the following case: constant force acts on the body. variable force acts on the body. (i) when (ii) When a 15. State the principle of conservation of momentum. Explain, why the gun recoil when a bullet is fired from it? 16.

4 Prove that the velocity of a rocket at any instant when its mass in m is given by, Where, and are the velocity and mass of rocket at t = 0 and u is the velocity of exhaust gases relative to the rocket. Also derive the expression for upthrust on rocket. 17. Derive the law of conservation of linear momentum from Newton s third law of motion. 18. What are concurrent forces? Obtain the condition for the equilibrium of three concurrent forces. 19. A rocket with a lift off mass 10,000 kg is blasted upward with an initial acceleration of 6 m/s 2. Calculate the initial thrust (force) of the blast.[ans.15.8 N] 20. A 20 g bullet moving at 300 m/s stops after penetrating 3 cm of bone. Calculate the average force exerted by the bullet.[ans. 3 ] 21. A bullet of mass 0.02 kg is fired from a gun weighing 7.5 kg. If the velocity of the bullet is 200 m/s, calculate the speed with which the gun recoils.[ans. 0.53m/s] 22. A bomb at rest explodes into three fragments of equal masses. Two fragments fly off at right angles to each other with velocities 9 m/s and 12 m/s respectively. Calculate the speed of third.[ans.15 m/s] 23. A rubber ball of mass 100 g falls from a height of 1m and rebounds to a height of 40 cm. Find the impulse and the average force between the ball and the ground, if time during which they are in contact was 0.1 s. [Ans Ns; N] 24. A rocket burns 0.5 kg of fuel per second, ejecting it as a gas with a velocity of 1600 m/s relative to the rocket. How much force is exerted on the rocket? Also calculate the velocity attained by the 25. rocket when its mass reduces to of its initial mass. [Ans.800 N;8.48 km/s] An elevator weighs 3000 kg. When the upward tension in the supporting cable is N, what is the upward acceleration? Starting from rest, how far does it rise in 2 second? Take g = 10 m/s 2.[Ans.5 m/s 2 ; 10 m].

5 Assignment Work (Physics) Class :Xi Chapter :05: LAWS OF MOTION(FRICTION & CIRCULAR MOTION) 1. Why are lubricants used in machines? 2. Ball bearing are used in machinery. Why? 3. Why wheels are made circular? Explain. 4. A man is at rest in the middle of a pond of perfectly frictionless ice. How can he get himself on the shore? 5. What is friction? Which is more: sliding friction or rolling friction? 6. What difference between dry friction and wet friction? 7. What is limiting friction? State the laws of limiting friction. 8. Define angle of friction and angle of response. Derive relationship between them. 9. What are the various methods of reducing friction? 10. A force of 50 kgf is required to pull a roller weighing 500 kg over ice. What is coefficient of friction? [Ans. 0.1 ] 11. A block slide down an inclined plane of slope angle 12. projected up the same plane with an initial velocity [Ans. ] with constant velocity. It is then. How far up the incline will it move? What is the acceleration of a block sliding down 30 0 slope when the coefficient of friction is Take g = 9.8 m/s 2. [Ans m/s 2 ] 13. Define angular displacement and angular velocity and then derive relation between linear velocity and angular velocity. Also explain that angular velocity is also known as angular frequency.

6 What is meant by centripetal acceleration? Derive the formula for centripetal acceleration? 14. Define centripetal force. Obtain an expression for centripetal force. Also explain centrifugal force. 15. Calculate the angular speed of (i) minutes hand and (ii) seconds hand of the clock. [Ans. 16. ] A flywheel makes 120 rpm. Find the angular speed of any point on the wheel and the linear speed of a point 10 cm from the centre of the wheel. [Ans.4 rad/s;40 cm/s] 17. A body of mass 0.10 kg is being rotated in a circular path of diameter 1.0 m on a frictionless horizontal plane by means of string. It performs 10 revolutions in 31.4 s. Calculate the centripetal force acting on the body. [Ans.0.2 N] 18. A mass of 500 g is going in a vertical circle of radius 80 cm so that the velocity at the top is 1 m/s. What is the tension and the centripetal force at the top and bottom? [Ans. 0 N; 29.4 N; 4.9 N;24.5 N] 19. A motor car of mass 1000 kg runs under a bridge at 48 km/h, the roadway in the form of an arc of radius 20 m. Find the reaction between the car and the road at the lowest point of the car. [Ans N]

7 Assignment Work (Physics) Class :Xi Chapter :06: WORK, POWER AND ENERGY 1. Why a coolie does no work when he moves on a level road while carrying a box on his head? 2. When an arrow is shot from its bow, it has kinetic energy. From where, does it get this kinetic energy? 3. A boy has a bag of sand of mass 20 kg. First of all, he keeps the bag on his head and moves 10 metre. Second time, he drags the bag through 10 metres on a frictionless surface. In which case, he does more work? 4. Which type of energy is lost in doing work against friction? 5. A stone is dropped from the top of a high tower. Will the mechanical energy of the stone be conserved or not if the force of friction due to air is not neglected? 6. Explain the term work. Show that work done is equal to the dot product of force and displacement. 7. What is meant by positive work, negative work and zero work? Give one example of each. 8. Define kinetic energy. Derive an expression for kinetic energy of the body. 9. State and prove Work Energy theorem. 10. Derive an expression for potential energy of the body. 11. Show that the total energy of a body falling freely under gravity is constant. 12. Derive the expression for potential energy of a stretched string. 13. State the principle of conservation of mechanical energy and show that this principle is valid in the case of a falling body. 14. What do you mean by power? Give its units and dimension. Derive the expression for power in term of force and velocity. 15. What do you mean by collision? What are elastic and inelastic collisions? Give example.

8 Discuss the elastic collision of two bodies in one dimension. Calculate the velocities of the bodies after the collision. Discuss, what happens when both the bodies are of equal mass. 16. What is an inelastic collision? A moving body collides with a stationary body of different mass. After perfectly inelastic collision, both the bodies stick together and move with a common velocity. Derive an expression for this common velocity. Also derive an expression for the loss in kinetic energy during the collision A force is applied on a body which is sliding over a floor. If the body is displaced through m, how much work is done by the force? [Ans. ] A rain drop of radius 2 mm falls from a height of 250 m above the ground. What is the work done by the gravitational force on the drop? [8.2 J] 19. A man pushes a roller with a force of 60 N through a distance of 30 m. Calculate the work done if the handle of the roller is inclined at an angle of 60 0 with the ground. [Ans. 900 J] 20. A body of mass 200 g is connected to the free end of a spring with force constant of 5 N/m. The body is pulled so that the spring stretches through a distance of 10 cm. The body is then left with zero initial velocity and the body moves towards its equilibrium position. Find the velocity of the body when it is at a distance of 8 cm from its mean position. [Ans. 0.3 m/s] 21. A bullet of mass m moving with velocity v is embedded into a block of mass M suspended by a thread. As a result of this collision the block (along with the bullet) comes in motion and rises to a height h. Prove that the velocity of the bullet was. 22. A train of mass 2000 quintal is drawn up an inclined plane of 2 in 100 at the rate of 72 km/h. If the resistance due to friction is 2500 N, calculate the power of the engine.[ans.834 kw] 23. An electric motor creates a tension of 4500 N in a hoisting cable and reels it at a rate of 2 m/s. Calculate the power of the motor. [Ans. 9 kw]

9 24. A bomb explodes into two fragments of masses 2.0 kg and 1.0 kg. The total kinetic energy of the fragments is 3.0 J. Calculate (i) kinetic energy of the bigger fragment, (ii) momentum of the smaller fragment.[ans. (i) 1.0 (ii) ] There is a head on collision between a 5 kg mass moving with a velocity of 10 m/s and a 5 kg mass at rest. Calculate velocities of the masses after the collision. [Ans. Zero and 10 m/s]

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