Title 4. Motion in a Plane.pdf ✅

1. The resultant of two vectors P and Q is R . If Q is doubled then the new resultant vector is perpendicular to ‘ P ’. R is equal to 2. 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:- (1) 45° (2) 60° 3. A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about:- (1) 2.5 m (2) 5 m (3) 7.5 m (4) 10 m 4. Two stones are projected with the same speed but making different angles with the horizontal Their ranges are equal. If the angle of projection of one is /3 and its maximum height is h1, then the maximum height of the other will be : (1) 3h1 (2) 2h1 (3) h1/2 (4) h1/3 5 . In projectile motion, the modulus of rate of change of velocity– (1) is const ant (2) first increases then decreases (3) first decreases then increases (4) None of t he above 6. If A B, and C are vectors having a unit magnitude. If A B C + + = 0 then A.B B.C+ C.A + will be :- (1) 1 (2) 3 2 (3) 1 2 (4) zero 7. An object is in equilibrium under four concurrent forces in the directions as shown in the figure. Magnitudes of F1 and F2 are 8. Two balls are projected from the same point simultaneously. First ball is projected vertically upwards and the second ball at an angle of projection 60° to the ground level. Both the balls reach the ground simultaneously. The ratio of their velocities are : (1) 1 : 2 (2) 3 : 2 (3) 3: 2 (4) 2 : 3 9. 1 2 3 A a i a j a k ˆ ˆ ˆ = + + and 1 2 3 B b i b j b k ˆ ˆ ˆ = + + .If A is parallel to B , then which of the following is correct :- 10. Let the angle between two nonzero vectors A and B be 120° and resultant be C :- (1) C must be equal to A B− (2) C must be less than A B− (3) C must be greater than A B− (4) C may be equal to A B− A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion. B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion. C. If Assertion is True but the Reason is False. D. If both Assertion & Reason are False. Motion in a Plane
11. Assertion :- A null vector is a vector whose magnitude is zero and direction is arbitrary. Reason :- A null vector does not exist. (1) A (2) B (3) C (4) D 12. A projectile is given an initial velocity of ( ) i j ˆ ˆ + 2 m/s, where ˆ i is along the ground and ˆ j is along the vertical. If g = 10 m/s2, the equation of its trajectory is : (1) y = x – 5x2 (2) y = 2x – 5x2 (3) 4y = 2x – 5x2 (4) 4y = 2x – 25x2 13. When n vectors of different magnitudes are added, we get a null vector. Then the value of n cannot be (1) 11 (2) 4 (3) 3 (4) 2 14. The vertical height Y and the horizontal distance X along the horizontal plane of a projectile thrown in air with point of projection at origin (ignoring resistance due to air) are given by : Y = 8t – 5t2 , X = 6t The angle of projection of this projectile is (1) tan–1 (8/5) (2) tan–1 (4/3) (3) tan–1 (5/6) (4) tan–1 (3/4) 15. A projectile has a horizontal range R when thrown at two different angles  and (90° – )If h1 and h2 are the maximum heights reached, then 16. A point source P moves counter clockwise on a circular path as shown in the figure. The movement of P is such that it sweeps out a length s = t3 + 5, where s is in metre and t is in seconds. The radius of path is 20 m. The acceleration of P when t = 2 is nearly. (1) 14 m/s2 (2) 13 m/s2 (3) 12 m/s2 (4) 7.2 m/s2 17. A particle moves along positive branch of curve 2 , 2 x y = where 2 2 t x = x and y are measured in metres and t in seconds. Velocity of the particle at t = 2s is :- 18. A particle is moving along a circular path. The angular velocity , linear velocity, angular acceleration and centripetal acceleration of the particle at any instant are   , , v and c a respectively. Which of the following relation is/are correct ? (1) a, b, d (2) b, c, d (3) a, b, c (4) a, c, d 19. A boat is moving in direction of vector 4 3 ˆ ˆ − +i j with a speed of 10 m/sec. Velocity vector of boat can be expressed as :- A B− 20. Two bullets are fired horizontal in vaccum with different velocities from the same height. Which will reach the ground first ? (1) Slower one (2) Faster one (3) Both will reach simultaneously (4) It cannot be predicted 21 . A body of mass 1 kg crosses a point O with a velocity 60 ms–1 . A force of 10 N directed towards O begins to act on it. It will again cross O in (1) 24 s (2) 12s (3) 6s (4) will never return to O 22. Given that A B C + + = 0 . Out of these three vectors two are equal in magnitude and the magnitude of the third vector is 2 times as that of either of the two having equal 2 magnitude. Then the angles between vectors are given by : (1) 30 ,60 ,90 o o o (2) 45 ,45 ,90 o o o
(3) 45 ,60 ,90 o o o (4) 90 ,135 ,135 ooo 23. Projection of vector A on B is: - (1) A B. (2) ˆ A B. (3) B A (4) B A ˆ ˆ  24. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is : 25. Find angle between a n d Z-axis :- 26. The ceiling of a tunnel is of 5 m high. What is the maximum horizontal distance that a ball thrown with a speed of 20 m/s, can go without hitting the ceiling of the tunnel ? (Take g = 10m/s2 ) (1) 30 m (2) 40 m (3) 30 2m (4) 20 2m 27. A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle 30° with the horizontal. How far from the throwing point will the ball be at the height of 10m from the ground ? (g =10 m/s2 ) (1) 5.20 m (2) 4.33 m (3) 2.60 m (4) 8.66 m 28. The position vector of a particle is given as The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to : (1) 1 sec (2) 2 sec (3) 1.5 sec (4) Not possible 29. Two particles are projected from the same point with the same speed at different angles 1 2   and to the horizontal. They have the same range. Their times of flight are t1 and t2 respectively. (4) All of the above 30. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal accelerations is : (1) 1 : 1 (2) m1 : m (3) m1 : m2 (4) r1 : r2 31. A ball is thrown at an angle  and another ball is thrown at an angle ( ) 0 90 − with the horizontal from the same point with same speed 40ms–1 . The second ball reaches 50m higher than the first ball. Find their individual heights? (1) 15m, 65m (2) 25m, 75m (3) 10m, 60m (4) 20m, 70m 32. A body is projected at an angle  with horizontal, another body is projected with the same speed at an angle  with the vertical then the ratio of the maximum height is :- (1) 1 : 1 (2) tan2  : 1 (3) 1 : cot  (4) none of these 33. A steam boat goes across a lake and comes back: (i) on a quiet day when the water is still and (ii) on a rough day when there is a uniform current so as to help the journey onward and to impede the journey back. If the speed of the launch, on both days, was same, the time required for the complete journey on the rough day as compared to that on the quiet day, will be :- (1) less (2) same (3) more (4) cannot be predicted 34. If the vectors ˆ ˆ ˆ P ai aj k = + + 3 and ˆ ˆ ˆ Q ai j k = − − 2 are perpendicular to each other then the positive value of a is :-
(1) zero (2) 1 (3) 2 (4) 3 35. If the angle between the vectors A and B is  ,the value of the product (B A A . .) is equal to:- (1) BA2 cos  (2) BA2 sin  (3) BA2 sin  cos  (4) zero 36. 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 :- (1) 0° (2) 30° (3) 45° (4) 60° 37. At the uppermost point of a projectile its velocity and acceleration are at an angle of :– (1) 180° (2) 90° (3) 60° (4) 45° 38. The vector sum of two force is perpendicular to their vector differences. In that case, the forces:- (1) Cannot be predicted (2) Are perpendicular to each other (3) Are equal to each other in magnitude (4) Are not equal to each other in magnitude 39. A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously 1 2 ˆ ˆ ˆ ˆ ˆ ˆ F i j k F i j k = − + = + + 5 5 5 , 2 8 6 , 3 4 ˆ ˆ ˆ ˆ ˆ ˆ F i j k F i j k = − + − = − − − 6 4 7 , 3 2 . Then the particle will move: (1) in X–Y plane (2) in Y–Z plane (3) in Z–X plane (4) along X–axis 40. Two projectile A and B are projected with angle of projection 15° for the projectile A and 45° for the projectile B. If RA and RB be the horizontal range for the two projectiles, then (1) RA < RB (2) RA = RB (3) RA > RB (4) the information is insufficient to decide the relation of RA with RB 41. The velocity of a particle is ˆ ˆ ˆ v i j k = + − 6 2 2 . The component of the velocity of a particle parallel to vector ˆ ˆ ˆ a i j k = + + is :- (1) ˆ ˆ ˆ 6 2 2 i j k + + (2) ˆ ˆ ˆ 2 2 2 i j k + + (3) ˆ ˆ ˆ i j k + + (4) ˆ ˆ ˆ 6 2 2 i j k + − 42. If the position vector of a particle is ˆ ˆ ˆ r ti tj tk = − + − cos sin 18 then what is the magnitude of its acceleration ? (1) 0 (2) 1 (3) sin2 t (4) cos t 43. In vector diagram shown in figure where ( R) is the resultant of vectors ( A) and ( B) If 2 B R = , then value of angle  is : (1) 30o (2) 45o (3) 60o (4) 75o