**HALF YEARLY EXAMINATION SAMPLE PAPER**

(QUESTIONS ARE FROM THE PART 1 NCERT TEXT BOOK)

CLASS: XI SUB: PHYSICS MM: 70 TIME: 3hrs.

**BLUE PRJNT**

Sl.No | Unit | VSA(1) | SA I (2) | SA II(3) | LA (5) | Total |

1 | Physical World& Measurement | 2(2) | 4(2) | 3(1) | ————- | 9(5) |

2 | Kinematics | 1(1) | 4(2) | 6(2) | 5(1) | 16(6) |

3 | Laws of Motion | 1(1) | 2(1) | 6(2) | ———– | 9(4) |

4 | Work,Energy and Power | 1(1) | 4(2) | 3(1) | 5(1) | 13(5) |

5 | Motion of System of Particles&Rigid Body | 2(2) | 4(2) | 3(1) | 5(1) | 14(6) |

6 | Gravitation | 1(1) | 2(1) | 6(2) | —————- | 9(4) |

Total | 8(8) | 20(10) | 27(9) | 15(3) | 70(30) |

*General instructions:*

*(i) **All questions are compulsory.*

*(ii) **There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9to18carry two marks each, questions 19to27carry three marks each and questions 28to30 carry five marks each. *

*(iii) **There is no overall choice. However, an internal choice has been provided in one question of two marks, in one question of three marks and all three questions of five marks each. You have to attempt only one of the given choice in such questions*

1. Name the fundamental force which is responsible for the stability of the nucleus. (1)

2. State the no. of significant figures in the following

a) 3.56 x 10^{-34 }b) 0.00005302 (1)

3. A pebble of mass 0.05kg is thrown vertically upwards. Given the direction and magnitude of the net force on the pebble,

(a) During its upward motion

(b) During its downward motion (1)

4. A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. Show that the power delivered to it at time‘t’ is proportional to‘t’. (1)

5. What is the moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end? (1)

6. Give the location of the centre of mass of a ring. Does the centre of mass of a body necessarily lie inside the body? (1)

7. Draw the position-time graph of an object moving with negative velocity. (1)

8. While considering the motion of an object under the gravitational influence of another object, which of the following quantities are conserved. (a) angular momentum (b) linear momentum (c) total mechanical energy (1)

9. The resistance R=V/I where V= (100 ±5) V, I= (10±0.2). Find the percentage error in R. (2)

10. Check the dimensional consistency of the equation. (2)

11. Fig shows the x-t plot of one dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t<0 and in a parabolic path for t>0? If not suggest a suitable physical context for this graph. (2)

12. The position of particle is given by **r**=3t **î **+ 2t^{2}ĵ + 5ǩ, where‘t’ is in seconds and the coefficients have proper units for ‘r’ to be in meters. Find V (t) and a (t) of the particle. (2)

13. What is impulse of a force, how it is related to momentum. (2)

14. The potential energy function for a particle executing linear simple harmonic motion is given by V(x)=kx^{2}/2, where k is force constant of the oscillator. For k=0.5Nm^{-1} the graph of V_{(x)} versus ‘x’ is as shown in figure. Show that a particle of total energy 1J moving under this potential must ‘turn back’ when it reaches ±2m.

OR

A body constrained to move along the Z-axis of a co-ordinate system is subject to a constant force F given by .What is the work done by this force in moving the body through a distance of 4m along the Z-axis? (2)

15. Prove work-energy theorem for a constant force. (2)

16. Define centre of gravity of a rigid body. (2)

17. What are the factors on which the moment of inertia of a body depends? (2)

18. Does the escape speed of a body from the earth depend on a) mass of the body b0 the height of the location of the body from where the body is launched? Justify . (2)

19. State Kepler’s laws of planetary motion. (3)

20. Explain the variation of acceleration due to gravity with a) altitude b)depth (3)

21. State i) theorem of parallel axes ii)theorem of perpendicular axes (3)

22. A pump on the ground floor of a building can pump water to fill a tank of volume30m^{3} in 15minutes.If the tank is 40m above the ground, and the efficiency of the pump is 30℅, how much electric power is consumed by the pump? (3)

23. Explain why a) a horse cannot pull a cart and run in empty space b) a cricketer moves his hands backwards while holding catch. (3)

24. a) State Newton’s second law of motion.

b) A bullet of mass 0.04 kg moving with a speed of 90ms^{-1} enters a heavy wooden block and is stopped after a distance of 60cm.What is the average resistive force exerted by the block on the bullet? (3)

25. Two bodies are thrown with the same initial velocity at angles α and ( 90^{o}-α) with the horizontal. What will be the ratio of i) maximum heights attained by them and ii) of horizontal ranges.

OR

What is a projectile? Show that the path of the projectile is parabolic. (3)

26. Explain any two uses of dimensional equations. Write any two of its limitations. (3)

27. A woman starts from her home at 9:00 am walks with a speed of 5km h^{-1} on a straight road up to her office 2.5 km away, stays at the office up to 5:00 pm and returns home by an auto with a speed of 25km h^{-1}.Choose suitable scales and plot the x-t graph of her motion. (3)

28. a) What is uniform circular motion? Find the magnitude and direction of centripetal acceleration in case of uniform circular motion of an object.

OR

a) Find the magnitude and direction of the resultant of two vectors **A **and** B **in terms of their magnitudes and angle θ between them.

b) A motor boat is racing towards north at 25kmh^{-1} and the water current in that region is 10kmh^{-1} in the direction of 60^{o} east of south. Find the resultant velocity of the boat. (5)

29. Obtain an expression for the potential energy of a spring and discuss the nature of its variation. Show that the total energy of the spring is constant in all positions. Show graphically the variation of PE, KE and TE with distance from the mean position.

OR

a) Answer the following questions with reasons:

i) In an elastic collision of two billiard balls, is the total kinetic energy is conserved during the short time of collision of the balls (i.e when they are in contact)?

ii) Is the total momentum is conserved during the short time of an elastic collision of two balls.

b) Give a brief account of elastic collision in two dimensions. (5)

30. a) Three bodies a ring ,a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

b) Given moment of inertia of a disc about any of its diameters to be MR^{2}/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

c) Find the moment of the sphere about a tangent to the sphere, given moment of inertia of the sphere about any of its diameters to be 2MR^{2}/5.

OR

a) Establish a relation between (i) torque and moment of inertia of a rigid body

(ii) Angular momentum and moment of inertia of a rigid body

b) A solid cylinder of mass20kg rotates about its axis with angular speed 100rad/s. The radius of the cylinder is 0.25m.What is the kinetic energy associated with rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis? (5)

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