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General Instructions:
(i) All questions are compulsory.
(ii) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions 9 to 18 carry two marks each, questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each.
(iii) There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all three questions of five marks each. You have to attempt only one of the given choices in such questions.
(iv) Use of calculators is not permitted.

Q.1.Can a body be in equilibrium when only one force acts on it? (1 mark)
Q.2. Is the average speed of a moving object during a given interval of time is always “the distance covered during the time interval divided by the time interval”? (1 mark)
Q.3. If a man in an elevator drops his briefcase but it does not fall to the floor, what can he conclude about the elevator’s motion? (1 mark)


Q.4. A boy wishes to row across a river in the shortest possible time. He can row at 2m/s in still water and the river is flowing at 1m/s. At what angle ? should he point the bow (front) of his boat?
(1 mark)

Q.5. What is the maximum value of gravitational potential energy and where?
(1 mark)

Q.6. A ring and a circular disc of different materials have equal masses and equal radii. Which one will have a larger moment of inertia about an axis passing through its centre of mass perpendicular to its plane? (1 mark)


Q.7. During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3, where the time t is in seconds. Find out the units of a and b.
(1 mark)

Q.8 A heavy ball is suspended as shown. A quick jerk on the lower string will break that string but a slow pull on the lower string will break the upper string. Why the first result occurs? Give the reason only in one sentence.
(1 mark)



Q.9 Two forces, one with a magnitude of 3N and the other with a magnitude of 5N, are applied to an object. For which orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least? Give the reason for your answer in one line only.
(2 marks)


Q.10. What is the average kinetic energy of a molecule of a gas at a temperature of 400K? (2 marks)
Q. 11. Two bodies on the two sides of an equal-arm balance exactly balance each other. If the balance is placed in an elevator and given an upward acceleration, do they still balance? Justify your answer.
(2 marks)

Q.12. Suppose A = BnCm, where A has dimensions [M0L+1T+1], B has dimensions [M0L+2T-1], and C has dimensions [M0L+1T+2]. Then find out the values of exponents n and m.
(2 marks)


Q.13. Derive an expression for moment of inertia of a uniform rod about an axis perpendicular to the length of the rod and passing through its centre.
(2 marks)
OR

A solid cylinder rolls without slipping down a plane inclined at an angle ‘?’ to the horizontal. What is the linear acceleration of its center of mass? ( 2 marks)

Q.14. Suppose a tunnel is drilled completely through the earth along a diameter. Mass and radius of earth are Me and Re. What is the force acting on a body of mass m at a distance x from the centre of earth? ( 2 marks)

Q.15. Why are space rockets usually launched from west to east in the equitorial plane? (2 marks)
Q. 16. Establish equation of continuity of an ideal liquid flow. ( 2 marks)
Q. 17. Why does oil spread over the surface of water? Explain. ( 2 marks)
Q.18. What is a simple harmonic motion? State its characteristics. (2 marks)
Q.19. In the diagram, has magnitude 12m and has magnitude 8m. Find out the x component of .
(3 marks)



Q. 20. The system shown remains at rest. Each block weighs 20 N. Calculate the force of friction on the Block kept on the inclined plane.
(3 marks)

Q.21. Prove that when a very heavy particle makes a perfectly elastic head-on collision with a very light particle that is at rest, the light one goes off with twice the velocity of the heavy one.
( 3 marks)

Q.22. i) A compressed spring is clamped in its compressed position and it then dissolved in acid, what becomes of its elastic potential energy?



ii) An automobile of mass m accelerates, starting from rest, while the engine supplies constant power ‘ P’ . Show that the velocity ‘v’ is given by equation
( 2 + 1 marks)


Q.23 i) What is meant by degrees of freedom? ( 1 mark)
ii) State law of equipartition of energy. ( 1 mark)
iii) Write any two characteristics of an ideal gas. ( 1 mark)

Q.24. Experienced cooks can tell whether an egg is raw or hard-boiled by rolling it down a slope. How is this possible? (3 marks)


Q.25. Establish the relationship among coefficient of linear expansion (a), coefficient of superficial expansion (ß) and coefficient of volumetric expansion ( ?). (3 marks)


Q. 26. i) Stainless steel cooking pans are preferred with extra copper bottoms.
Why? ( 1 mark)
ii) At what temperature is the Fahrenheit scale reading equal to half that
of the Celsius scale? Calculate. ( 2 marks)

Q.27. Two identical wires of sitar have a fundamental frequency of 500 Hz, when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 50 beats/ sec when both wires oscillate simultaneously? ( 3 marks)
OR
Find the expressions for time period and frequency in the oscillations of a liquid in a U-tube. ( 3 marks)

Q.28. i) What is a projectile? Give its examples. ( 1 mark)
ii) Show that the path of projectile is a parabolic path when projected
obliquely from a certain point on the ground. ( 3 marks )

iii) At what point of its trajectory, the speed of projectile is minimum?
( 1 mark)
OR
i) The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h. At what distance ‘d’ should it release a heavy bomb to hit the target X? Take g = 10 m/s2.
( 3 marks)
ii) Find the angle of projection for a projectile motion whose range R is 4 times the maximum height H.
( 2 marks)

Q.29. i) What is a heat engine? ( 1 mark)
ii) Briefly describe four steps of a Carnot’s cycle. ( 2 marks)
iii) Derive an expression for the efficiency of Carnot’s heat engine, in terms
of temperatures of source and sink. ( 2 marks )
OR
i) When a gas expands adiabatically, it does work on its surroundings. But if
there is no heat input to the gas, where does the energy come from?
( 2 marks)

ii) An ideal gas undergoes an isothermal expansion at 00C from 0.010m3 to 0.200 m3. For 5 mole of gas ,compute

a) the work done b) the heat added and c) the change in internal energy.
{Given that Log10 20= 1.3010} (1 + 1+ 1 mark)


Q.30. The equation of a transverse travelling wave on a string is

Where x and y are in cm. and t is in seconds. Find
i) amplitude ii) wavelength iii) frequency iv) time period v) wave velocity
( 1+1+1+1+1 mark)
OR
Discuss analytically (ie. prove the equation of a standing wave) formation of
standing waves on stretched string.
( 5 marks )