(c) D. (d) 2D. 2. A body is moving along a circular path with variable speed. It has. (a) a radial acceleration. (b) a tangential acceleration

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1 1. A body is allowed to slide on a frictional less track from rest under-gravity. The track ends in a circular loop of diameter D. What should be the minimum height of the body in terms of D, so that it may successfully complete the loop? (a) D D (c) D 2D 2. A body is moving along a circular path with variable speed. It has (a) a radial acceleration a tangential acceleration (c) zero acceleration both tangential and radial accelerations 3. A body is traveling in a circle at constant speed. It (a) has constant velocity. has no acceleration (c) has an inward acceleration has an outward radial acceleration 4. A body of mass 100 gram, tied at the end of a string of length 3 m rotates in a vertical circle and is just able to complete the circle. If the tension in the string at its lowest point is 3.7 N, then its angular velocity will be (g = 10 m/s2) (a) 4 rad/s 3 rad/s (c) 2 rad/s

2 1 rad/s 5. A body of mass 500 gram is rotating in a vertical circle of radius 1 m. What is the difference in its kinetic energies at the top and the bottom of the circle? (a) 4.9 J 19.8 J (c) 2.8 J 9.8 J 6. A body of mass m is suspended from a string of length l. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete full revolution in the vertical plane with the point of suspension at the center of circle? (a) (c) 7. A body of mass m performing UCM with frequency n along the circumference of circle having radius r, force is given by (a) 4 nm n 2 m (c) 2 n 2 mr nm 2

3 8. A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical circle. What should be the minimum velocity of the bucket at the highest point, so that the water in the bucket will not spill? (g = 10 m/s2) (a) 2.5 m/s 4 m/s (c) 5 m/s 7 m/s 9. A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with a constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position? (a) 4 m/sec m/sec. (c) 16 m/sec. None of these 10. A can filled with water is revolved in a vertical circle of radius 4 metre and the water does not fall down. The time period of revolution will be (a) 1 sec 10 sec (c) 8 sec 4 sec 11. A car has a linear velocity v on a circular track of radius r. If its speed is increasing at a rate of a m/s2, then its resultant acceleration will be (a)

4 (c) 12. A car is moving in a circular track of radius 10 metre with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of 1 metre long. The angle made by the rod with the track is (a) zero 30 (c) A car is moving in horizontal circular track of radius 10 m, with a constant speed of 36 km/hour. A simple pendulum is suspended from the roof of the car. If the length of the simple pendulum is 1 m, what is the angle made by the string with the track? (a) (c) A car is moving on a circular path and takes a turn. If R1 and R2 are the reactions on the inner and outer wheels respectively, then (a) R 1 = R 2 R 1 < R 2

5 (c) R 1 > R 2 R 1 R A car is moving with a speed of 30 m/s on a circular path of radius 500 m. Its speed is increasing at the rate of 2 m/s2. The acceleration of the car is (a) 9.8 m/ s m/ 2 (c) 2 m/s m/s A car moving on a horizontal road may be thrown out of the road is taking a turn (a) by the gravitational force due to the lack of proper centripetal force (c) due to the lack of frictional force between the tire and the road due to the reaction of the ground 17. A car of mass 1000 kg moves on a circular road with a speed of 20 m/s. Its direction changes by 90 after traveling 628 m on the road. The centripetal force acting on the car is (a) 500 N 1000 N (c) 1500 N 2000 N 18. A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then maximum velocity with which the car can move is (a) 7 m/s

6 14 m/s (c) 8 m/s 12 m/s 19. A car sometimes overturns while taking a turn. When it overturns, it is (a) the inner wheel which leaves the ground first the outer wheel which leaves the ground first (c) both the wheel leave the ground simultaneously either inner wheel or the outer wheel leaves the ground 20. A coin kept on a rotating gramophone disc just begins to slip if its centre is at a distance of 8 cm from the centre of the disc. The angular velocity of the gramophone disc is then doubled. Through what distance, the coin should be shifted towards the centre, so that the coin will just slip? (a) 2 cm 4 cm (c) 6 cm 16 cm 21. A cyclist goes round a circular path of circumference 343 m in s. The angle made by him, with the vertical is (a) (c) A cyclist is moving in a circular track of radius 80 m, with a velocity of 36 km/hour. In order to keep his balance, he has to lean inwards from the vertical through an angle. If g = 10 m/s2, then q is given by

7 (a) tan 1 (2) tan 1 (4) (c) tan 1 tan A cyclist turns around a curve at 15 miles per hour. If he turns at double the speed, the tendency of overturn is (a) doubled quadrupled (c) halved unchanged 24. A fighter aeroplane flying in the sky dives with a speed of 360 km/hr in a vertical circle of radius 200 m. Weight of the pilot sitting in it is 75 kg. What will be the value of force with which the pilot presses his seat when the aeroplane is at highest position (g = 10 m/ s 2 ) (a) 3000 N 1500 N (c) (75 g)n 300 N 25. A frictional track ABCDE ends in a circular loop of radius R, body slides down the track from point A which is at a height h of 5 cm. Maximum value of R for the body to successfully complete the loop is: (a) 5 cm cm

8 (c) cm 2 cm Ans. 1 to B 2. D 3. C 4. B 5. D 6. D 7. B 8. C 9. A 10. D 11. A 12. C 13. B 14. B 15. D 16. C 17. B 18. B 19. A 20. A 21. D 22. D

9 23. B 24. B 25. D 26. A thief stole a box with valuable article of weight W and jumped down a wall of height h. Before he reach the ground he experienced a load of (a) zero W / 2 (c) W 2 W 27. The acceleration due to gravity g and mean density of the earth r are related by which of the following relation? Where g is gravitational constant and R is radius of the earth (a) = = (c) = = 28. When the planet comes nearer the sun moves (a) fast slow (c) constant at every point none of the above

10 294. Kepler s second law regarding constancy of arial velocity of a planet is a consequence of the law of conservation of (a) energy angular momentum (c) linear momentum none of these 30. The period of geostationary artificial satellite is (a) 24 hours 6 hours (c) 12 hours 48 hours 31. A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5 R from the surface of earth is (a) 6 hr 6 hr (c) 5 hr 10 hr 32. The distance of Neptune and Saturn from the sun are nearly m and m respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of (a)

11 (c) A satellite is orbiting close to the surface of the earth, then its speed is (a) Rg (c) 34. If the gravitational force between two objects were proportional to 1/R (and not as 1/R 2 ) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to (a) R 0 (c) R Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to then (a) T 2 R 2 T 2 (c) T 2

12 T 2 R The period of a satellite in a circular orbit of radius R is T. The period of another satellite in circular orbit of radius 4R is (a) T/4 8T (c) 2T T/8 37. A planet moves around the sun. At a point A, it is closest from the Sun at a distance d 1 and has a speed v 1. At another point B, when it is farthest from the sun at a distance d 2, its speed will be (a) (c) 38. The period of geostationary artificial satellite of earth is (a) 6 hours 12 hours (c) 24 hours 365 days

13 39. If r represents the radius of the orbit of a satellite of mass m moving round a planet of mass M, the velocity of the satellite is given by (a) v 2 = v 2 = (c) v = v = 40. A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is (a) Positive Negative (c) Zero may be positive or negative 41. The escape velocity of projection from the earth is approximately (R = 6400 km) (a) 7 km/sec 112 km/sec (c) 12.2 km/sec 1.1 km/sec 42. If the earth is 1/4 th of its present distance from the sun, the duration of the year would be (a) 1/4 of the present year 1/6 of the present year

14 (c) 1/8 of the present year 1/16 of the present year 43. The relation between escape velocity and orbit velocity is (a) v e = v e = v orb (c) v e = 2v orb v e = v orb 44. There is no atmosphere on the moon because (a) it is closer to the earth it revolves round the earth (c) it gets light from the sun the escape velocity of gas molecules is less than their root mean square velocity here 45. If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth s surface would (a) decrease by 2% remain unchanged (c) increase by 2% will increase by 9.8% 46. F g and F e represents gravitational and electrostatic forces respectively, between the two electrons situated at a distance of 10 m. The ratio F g /F e is of the order of (a) 10 43

15 10 36 (c) The value of g at a particular point is 9.8 m/ sec 2 suppose the earth suddenly shrink uniformly to half its present size without losing any mass. The value of g at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will become (a) 9.8 m/sec m/sec 2 (c) 19.6 m/sec m/sec The planet mercury is revolving in an elliptical orbit around the sun as shown in figure. The kinetic energy of mercury will be greater at (a) A B (c) C D 49. The orbit velocity of an artificial satellite in a circular orbit just above the earth s surface is v. For a satellite orbiting at an altitude of half of the earth s radius, the orbital velocity is (a)

16 (c) 50. If the change in the value of g at the height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth) (a) x = h x = 2 h (c) x = x = h 2 Ans. 26 to (a) 27. (c) 28. (a) (a) 31. (a) 32. (c) 33. (c) (a)

17 38. (c) 39. (c) (c) 42. (c) 43. (a) (c) 46. (c) 47. (a) 48. (a) 49. (c) One end of a towel dips into a bucket full of water and other end hangs over the bucket. It is found that after some time the towel becomes fully wet. It happens (CPMT 86) (a) Because viscosity of eater is high Because of the capillary action of cotton threads (c) Because of gravitational force Because of evaporation of water. 52. For tap water and clean glass, the angle of contact is (a) 0 90 (c) Water rises up to a height h1 in a capillary tube of radius r. the mass of the water lifted in the capillary tube is M. if the radius of the capillary tube is doubled, the mass of water that will rise in the capillary tube will be

18 (a) M 2M (c) 4M 54. Water rises through a height h in a capillary tube of internal radius (r). if T is the S.T. of water, then the pressure difference between the liquid level in the container and the lowest point of the concave meniscus is (a) (c) 55. A number of small drops of mercury coalesce adiabatically to form a single drop. The temperature of drop (a) Increases Is infinite (c) Remains unchanged May decrease or increase depending upon size 56. The angle of contact between a glass capillary tube of length 10 cm and a liquid is 90. If the capillary tube is dipped vertically in the liquid, then the liquid (a) Will rise in the tube Will get depressed in the tube (c) Will rise up to 10 cm in the tube and will over flow Will neither rise nor fall in the tube Answer: 57. When there are no external forces, the shape of a liquid drop is determined by (a) Surface tension of the liquid

19 Density of liquid (c) Viscosity of liquid Temperature of air only 58. If T is surface tension of soap solution, the amount of work done in blowing a soap bubble from diameter D to a diameter 2D is (PMT MP 90) (a) 2 D 2 T 4 D 2 T (c) 6 D 2 T 8 D 2 T 59. Choose the wrong statement from the following. (a) Small droplets of a liquid are spherical due to surface tension Oil rises through the wick due to capillarity (c) In drinking the cold drinks through a straw, we use the phenomenon of capillarity Gum is used to stick two surfaces. In this process we use the property of Adhesion Answer: (c) 60. If the surface of a liquid is plane, then the angle of contact of the liquid with the walls of container is (a) Acute angle Obtuse angle (c) A capillary tube when immersed vertically in a liquid records a rise of 3 cm. if the tube is immersed in the liquid at an angle of 60 with the vertical, then length of the liquid column along the tube will be (a) 2 cm 3 cm (c) 6 cm 9 cm 62. If sap bubbles of different radii are in communication with each other (PMT MP 88, NCERT 80) (a) Air flow from the larger bubble into the smaller one until the two bubbles are of equal size

20 The sizes of the bubbles remain unchanged. (c) Air flows from the smaller into the larger on and lager bubble grows at the expense of the smaller one Air flows from the larger into the smaller one becomes equal to that of the larger one and the large one equal to that of the smaller one. 63. A capillary tube of radius r can support a liquid of weight N. if the surface tension of the liquid is N/m. the radius of capillary must be (a) m m (c) m m 64. The work done in blowing a soap bubble of radius R is W1 and that to a radius 3R is W2. the ratio of work done is (a) 1:3 3:1 (c) 1:9 9:1 65. When the angle of contact between a solid and a liquid is 90, then (a) Cohesive force > Adhesive force Cohesive force < Adhesive force (c) Cohesive force = Adhesive force Cohesive force >> Adhesive force 66. Rain drops are spherical in shape because of (a) Surface tension Capillary (c) Downward motion Acceleration due to gravity

21 67. A sheet can be made water proof by coating it with a substance that changes the angle of contact (a) To zero (c) From acute to obtuse From obtuse to acute 68. Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by N, forces due to the weight of the liquid. If the surface tension of water is N/m, the inner-circumference of the capillary must be (a) m m (c) m m 69. What is the change in surface energy, when a mercury drop of radius R splits up into 1000 droplets of radius r? (a) 8 R 2 T 16 R 2 T (c) 24 R 2 T 36 R 2 T 70. Which of the following is not based one the principle of capillarity (a) Floating of wood on eater surface Ploughing of soil (c) Rise of oil in wick of lantern Soaking of ink by bloating paper 71. The rise of a liquid in a capillary tube does not depend upon (a) Angle of contact

22 Density of the liquid (c) Radius of the capillary tube Atmospheric pressure 72. The height of water in a capillary tube of radius 2 cm is 4 cm. what should be the radius of capillary, if the water rises to 8 cm in tube? (MHT-CET-2001) (a) 1 cm 0.1 cm (c) 2 cm 4 cm 73. The work done to get n smaller equal size spherical drops from a bigger size spherical size drop of water is proportional to (EAMCET 91) (a) (c) 74. For a liquid, which is rising in a capillary tube, the angle of contact is (a) (c) Acute Obtuse 75. W is the work done, when a bubble of volume V is formed from a solution. How much work is required to be done to form a bubble of volume 2V? (a) 2 W W (c) 2 1/3 W 4 1/3 W Ans. 51 to b 52. d 53. b

23 54. c 55. d 56. d 57. a 58. c 59. c 60. d 61. c 62. c 63. d 64. c 65. c 66. a 67. c 68. d 69. d 70. a 71. d 72. a 73. c 74. c 75. d