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Motion in a Plane Q1.

[1988] (a) π/2 (b) cos–1 0.6 (c) tan–17/5 (d) π/4 Ans: (a) Q2.

[1989] (a) A2B (b) zero (c) A2Bsin θ (d) A2Bcosθ Ans: (b) Q3. Abus is moving on a straight road towards north with a uniform speed of 50 km/hour turns through 90°. If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is [1989] (a) 70.7 km/hour along south-west direction (b) zero (c) 50 km/hour along west (d) 70.7 km/hour along north-west direction. Ans: (a) Q4. The maximum range of a gun of horizontal terrain is 16 km. If g = 10 ms–2, then muzzle velocity of a shell must be [1990] (a) 160 ms–1 (b) 200√2 ms-1 (c) 400 ms–1 (d) 800 ms–1 Ans: (c) Q5. Two bodies of same mass are projected with the same velocity at an angle 30° and 60° respectively. The ratio of their horizontal ranges will be [1990] (a) 1: 1 (b) 1: 2 (c) 1: 3 (d) 2: √2 Ans: (a)

Q6. An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is [1990] (a) 1600 ms–2 (b) 47.4 ms–2 (c) 23.7 ms–2 (d) 50.55 ms–2 Ans: (c) Q7. When milk is churned, cream gets separated due to [1991] (a) centripetal force (b) centrifugal force (c) frictional force (d) gravitational force Ans: (b) Q8.

[1992] (a) zero (b) A (c) zero vector (d) unit vector Ans: (c) Q9. If a body Aof mass Mis thrown with velocity v at an angle of 30° to the horizontal and another body Bof the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of horizontal range of Ato Bwill be [1992] (a) 1: 3 (b) 1: 1 (c) 1: √3 (d) √3:1 Ans: (b) Q10. Aboat is sent across a river with a velocity of 8 km h–1. If the resultant velocity of boat is 10 km h–1, then the velocity of the river is [1993] (a) 12.8 km h–1 (b) 6 km h–1 (c) 8 km h–1 (d) 10 km h–1 Ans: (b) Q11.

[1994] (a) 190 J (b) 160 J (c) 150 J (d) 20 J Ans: (c)

MockTime.com Q12. When a body moves with a constant speed along a circle [1994] (a) its velocity remains constant (b) no force acts on it (c) no work is done on it (d) no acceleration is produced in it Ans: (c) Q13.

[1995] (a) directed towards the origin (b) directed away from the origin (c) parallel to the position vector (d) perpendicular to the position vector Ans: (d) Q14. Which of the following is not a vector quantity? 1995 (a) speed (b) velocity (c) torque (d) displacement Ans: (a) Q15. Abullet is fired from a gun with a speed of 1000 m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s2) [1995] (a) 5 cm (b) 10 cm (c) 15 cm (d) 20 cm Ans: (a) Q16. A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on circular path [1996] (a) √2 m/s (b) 2 m/s (c) 10 m/s (d) 20 m/s Ans: (b) Q17. Aball whose kinetic energy is E, is thrown at an angle of 45° with the horizontal. Its kinetic energy at the highest point of its flight will be [1997] (a) E (b) E/2 (c) E/√2 (d) 0 Ans: (b) Q18.

[1997]

(a)

(b)

(c)

(d) Ans: (d) Q19.

[1998] (a) 5.8 m/s (b) 9.8 m/s (c) 10 m/s (d) 17.3 m/s Ans: (d)

Q20. Aball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved? [1998] (a) 14 m/s (b) 3 m/s (c) 5 m/s (d) 3.92 m/s Ans: (a) Q21. A500 kg car takes a round turn of radius 50 m with a velocity of 36 km/h. The centripetal force is [1999] (a) 250 N

MockTime.com (b) 750 N (c) 1000 N (d) 1200 N Ans: (c) Q22.

[1999]

(a)

(b)

(c)

(d) Ans: (b) Q23. 23. The angle between two vectors of magnitude 12 and 18 units when their resultant is 24 units, is 1999 (a) 63° 51’ (b) 75° 52’ (c) 82° 31’ (d) 89° 16’ Ans: (b) Q24. A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 1.2 m, then tension in the string when the body is at the top of the circle, is [1999] (a) 41.56 N (b) 89.86 N (c) 109.86 N (d) 115.86 N. Ans: (a) Q25. Astone tied with a string, is rotated in a vertical circle. The minimum speed with which the string has to be rotated [1999] (a) is independent of the mass of the stone (b) is independent of the length of the string (c) decreases with increasing mass of the stone (d) decreases with increasing length of the string Ans: (a) Q26. Aperson swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle 120° with the direction of flow of water. The speed of water in stream is [1999] (a) 1.0 m/s (b) 0.5 m/s (c) 0.25 m/s (d) 0.43 m/s. Ans: (c) Q27.

[1999] (a) 1 (b) √0.11 (c) √0.01 (d) 0.39 Ans: (b) Q28. Two projectiles are fired from the same point with the same speed at angles of projection 60° and 30° respectively. Which one of the following is true? [2000] (a) Their maximum height will be same (b) Their range will be same (c) Their landing velocity will be same (d) Their time of flight will be same Ans: (b) Q29.

[2000] (a) bottom point B (b) the point C (c) the point D (d) top point A Ans: (a) Q30.

[2000] (a) 45 J/s (b) 35 J/s (c) 25 J/s (d) 195 J/s Ans: (a) Q31. Aboat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is [1998, 2000] (a) 3 (b) 4 (c) √21 (d) 1 Ans: (a)

MockTime.com Q32. Achild is swinging a swing. Minimum and maximum heights of swing from earth’s surface are 0.75 m and 2m respectively. The maximum velocity of this swing is [2001] (a) 5 m/s (b) 10m/s (c) 15 m/s (d) 20m/s Ans: (a) Q33. Two particles of mass Mand m are moving in a circle of radii Rand r. If their time-periods are same, what will be the ratio of their linear velocities? [2001] (a) MR: mr (b) M: m (c) R: r (d) 1: 1 Ans: (c) Q34.

[1994, 2001] (a) zero (b) 45° (c) 90° (d) 180° Ans: (c) Q35. From a 10 m high building a stone 'A' is dropped, and simultaneously another identical stone 'B' is thrown horizontally with an initial speed of 5 ms–1. Which one of the following statements is true? [2002] (a) It is not possible to calculate which one of the two stones will reach the ground first (b) Both the stones ('A' and 'B') will reach the ground simultaneously (c) 'A' stone reaches the ground earlier than 'B' (d) 'B' stone reaches the ground earlier than 'A' Ans: (b) Q36.

[2002]

(a)

(b)

(c)

(d) Ans: (c) Q37. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces [2003]

(a) cannot be predicted (b) are equal to each other (c) are equal to each other in magnitude (d) are not equal to each other in magnitude Ans: (c) Q38. A particle moves along a circle of radius (20/π)m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is [2003] (a) 40 πm/s2 (b) 40 m/s2 (c) 640 πm/s2 (d) 160 πm/s2 Ans: (b) Q39.

[2004]

(a)

(b)

(c)

(d) Ans: (b) Q40.

[2004]

(a)

(b)

(c)

(d) Ans: (b) Q41.

[2005] (a) 1/2 (b) –1/2 (c) 1

MockTime.com (d) –1 Ans: (b) Q42.

[2005] (a) BA2 sinΘ (b) BA2 cosΘ (c) BA2 sinΘcosΘ (d) zero Ans: (d) Q43. Two boys are standing at the ends Aand Bof a ground where AB= a. The boy at Bstarts running in a direction perpendicular to ABwith velocity v1. The boy at Astarts running simultaneously with velocity v and catches the other boy in a time t, where t is [2005]

(a)

(b)

(c)

(d) Ans: (d) Q44. Astone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone? [2005] (a) π2 m s–2 and direction along the radius towards the centre (b) π2 m s–2 and direction along the radius away from the centre (c) π2 m s–2 and direction along the tangent to the circle (d) π2 /4 m s–2 and direction along the radius towards the centre Ans: (a) Q45. The circular motion of a particle with constant speed is [2005] (a) periodic but not simple harmonic (b) simple harmonic but not periodic (c) periodic and simple harmonic (d) neither periodic nor simple harmonic Ans: (a) Q46. Acar runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds in every circular loop. The average velocity and average speed for each circular loop respectively, is [2006] (a) 0, 10 m/s (b) 10 m/s, 10 m/s (c) 10 m/s, 0 (d) 0, 0 Ans: (a)

Q47. For angles of projection of a projectile (45° – θ) and (45° + θ), the horizontal ranges described by the projectile are in the ratio of [2006] (a) 1: 3 (b) 1: 2 (c) 2: 1 (d) 1: 1 Ans: (d) Q48.

[1991, 1996, 2001, 2006] (a) 60° (b) 75° (c) 45° (d) 90° Ans: (d) Q49. A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are (√3,3). The path of the particle makes with the x-axis an angle of [2007] (a) 45° (b) 60° (c) 0° (d) 30° Ans: (b)

Q50.

[2007] (a) 45° (b) 30° (c) 90° (d) 60° Ans: (d) Q51.

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[2008]

(a)

(b)

(c)

(d) Ans: (a) Q52. A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be: [2008] (a) 2mv (b) mv/√2 (c) mv √2 (d) zero Ans: (c) Q53.

[2010]

(a)

(b)

(c)

(d) Ans: (c) Q54.

[2010]

(a)

(b)

(c)

(d) Ans: (c) Q55. A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 πs. The acceleration of the particle is [2011] (a) 15 m/s2 (b) 25 m/s2 (c) 36 m/s2 (d) 5 m/s2 Ans: (d) Q56. A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is [2011] (a) 40 m (b) 50 m (c) 60 m (d) 20 m Ans: (a) Q57. A projectile is fired at an angle of 45° with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is [2011M]

(a)

(b)

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(c)

(d) Ans: (b) Q58. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectiles is: [2012]

(a)

(b)

(c)

(d) Ans: (b) Q59.

[2012]

(a)

(b)

(c)

(d) Ans: (b) Q60.

2013

(a)

(b)

(c)

(d) Ans: (b) Q61.

2013

(a)

(b)

(c)

(d) Ans: (d) Q1.

Q2.

Q3.

Q4.

Q5.

Q6.

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Q7.

Q8.

Q9.

Q10.

Q11.

Q12.

Q13.

Q14.

Q15.

Q16.

Q17.

Q18.

Q19.

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Q20.

Q21.

Q22.

Q23.

Q24.

Q25.

Q26.

Q27.

Q28.

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Q29.

Q30.

Q31.

Q32.

Q33.

Q34.

Q35.

Q36.

Q37.

Q38.

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Q39.

Q40.

Q41.

Q42.

Q43.

Q44.

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Q45.

Q46.

Q47.

Q48.

Q49.

Q50.

Q51.

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Q52.

Q53.

Q54.

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Q55.

Q56.

Q57.

Q58.

Q59.

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Q60.

Q61.