NEET UG - Resolution of a vector, relative velocity, motion in a plane, projectile motion Online Test (MCQ Quiz)

1. A vector can be resolved into its components along two non-collinear axes. If a vector A makes an angle θ with the x-axis, its component along the x-axis is given by:

A) A sin θ B) A cos θ C) A tan θ D) A

2. Two vectors are collinear if they are parallel or anti-parallel. If two vectors are collinear, their cross product is:

A) Zero B) Equal to their dot product C) Maximum D) Minimum

3. The relative velocity of object B with respect to object A is given by the formula:

A) v_B + v_A B) v_A - v_B C) v_B - v_A D) v_A + v_B

4. If two objects A and B are moving with velocities v_A and v_B respectively, their relative velocity when moving in the same direction is:

A) v_A + v_B B) v_A - v_B C) v_B - v_A D) Zero

5. When two objects A and B are moving in opposite directions with velocities v_A and v_B respectively, their relative velocity of approach is:

A) v_A - v_B B) v_B - v_A C) v_A + v_B D) Zero

6. A car is moving north at 60 km/h. A truck is moving south at 40 km/h. The relative velocity of the car with respect to the truck is:

A) 100 km/h South B) 20 km/h North C) 100 km/h North D) 20 km/h South

7. Motion in a plane involves displacement, velocity, and acceleration vectors that lie in the same plane. This type of motion is also known as:

A) One-dimensional motion B) Two-dimensional motion C) Three-dimensional motion D) Rotational motion

8. In projectile motion, the horizontal component of velocity is:

A) Zero B) Constant C) Increasing D) Decreasing

9. In projectile motion, neglecting air resistance, the vertical component of acceleration is:

A) Zero B) Equal to the horizontal acceleration C) Equal to 'g' downwards D) Equal to 'g' upwards

10. The path followed by a projectile is a:

A) Straight line B) Circle C) Parabola D) Ellipse

11. If a projectile is launched horizontally from a height h with initial velocity u, the time it takes to hit the ground depends on:

A) Only the initial velocity u B) Only the height h C) Both u and h D) The acceleration due to gravity g

12. The range of a projectile launched with initial velocity v at an angle θ with the horizontal is given by:

A) (v^2 sin(2θ))/g B) (v^2 cos(2θ))/g C) (v^2 tan(2θ))/g D) (v sin θ)/g

13. For a given initial speed, the maximum range of a projectile is achieved when the launch angle is:

A) 0 degrees B) 30 degrees C) 45 degrees D) 90 degrees

14. The maximum height reached by a projectile launched with initial velocity v at an angle θ with the horizontal is given by:

A) (v^2 sin^2 θ)/(2g) B) (v^2 cos^2 θ)/(2g) C) (v^2 tan^2 θ)/(2g) D) (v sin θ)/(2g)

15. If a projectile is launched vertically upwards with velocity v, the maximum height it reaches is:

A) (v^2)/(2g) B) (v^2)/g C) (2v^2)/g D) v/g

16. The time of flight of a projectile launched at an angle θ with initial velocity v is:

A) (2v sin θ)/g B) (v sin θ)/g C) (v cos θ)/g D) (2v cos θ)/g

17. A boat is crossing a river. The velocity of the boat relative to the water is 5 m/s and the velocity of the river flow is 2 m/s. If the boat moves perpendicular to the river flow, its resultant velocity with respect to the bank is:

A) 7 m/s B) 3 m/s C) sqrt(29) m/s D) sqrt(21) m/s

18. If a projectile is launched with velocity v at an angle θ and hits the ground at the same level, its velocity at the highest point is:

A) Zero B) v cos θ C) v sin θ D) v

19. When a particle moves in a plane with uniform speed, its acceleration is:

A) Zero B) Tangential C) Centripetal D) Both tangential and centripetal

20. Relative velocity is independent of the frame of reference, provided the frames are inertial. This is a consequence of:

A) Newton's first law B) Newton's second law C) Newton's third law D) Galilean transformations

21. A vector A can be written as A = Ax i + Ay j, where Ax and Ay are its components along the x and y axes respectively. The magnitude of vector A is given by:

A) sqrt(Ax^2 - Ay^2) B) sqrt(Ax^2 + Ay^2) C) Ax + Ay D) sqrt(Ax + Ay)

22. The angle α that vector A = Ax i + Ay j makes with the positive x-axis is given by:

A) tan α = Ay / Ax B) tan α = Ax / Ay C) sin α = Ay / A D) cos α = Ax / A

23. Two vectors are perpendicular if their dot product is:

A) Maximum B) Minimum C) Zero D) Equal to their cross product

24. If a vector is resolved into two perpendicular components, the sum of the squares of the magnitudes of the components is equal to the square of the magnitude of the original vector. This is based on:

A) Pythagorean theorem B) Trigonometric identity C) Vector addition rule D) Dot product definition

25. A man walks on a moving walkway. The speed of the man relative to the walkway is 1 m/s, and the speed of the walkway relative to the ground is 2 m/s. If the man walks in the same direction as the walkway, his speed relative to the ground is:

A) 1 m/s B) 2 m/s C) 3 m/s D) 0.5 m/s

26. If the man in the previous question walks in the opposite direction to the walkway, his speed relative to the ground is:

A) 1 m/s B) 2 m/s C) 3 m/s D) 0.5 m/s

27. For motion in a plane, the velocity vector can be resolved into horizontal and vertical components. If the velocity is v and makes an angle θ with the horizontal, then v_x = v cos θ and v_y = v sin θ. This is true when:

A) The motion is purely horizontal B) The motion is purely vertical C) The velocity is measured with respect to a stationary observer D) The velocity vector is considered in isolation

28. In projectile motion, the trajectory is parabolic because the horizontal motion is uniform (constant velocity) and the vertical motion is uniformly accelerated (due to gravity). This is a consequence of:

A) Newton's laws of motion B) Principle of superposition of velocities C) Conservation of energy D) Conservation of momentum

29. A projectile is launched with speed v at an angle θ. The velocity at any time t is given by:

A) v_x = v cos θ, v_y = v sin θ - gt B) v_x = v sin θ, v_y = v cos θ - gt C) v_x = v cos θ, v_y = v sin θ + gt D) v_x = v sin θ, v_y = v cos θ + gt

30. The position of a projectile at any time t, launched with velocity v at angle θ, is given by:

A) x = (v cos θ) t, y = (v sin θ) t - (1/2)gt^2 B) x = (v sin θ) t, y = (v cos θ) t - (1/2)gt^2 C) x = (v cos θ) t, y = (v sin θ) t + (1/2)gt^2 D) x = (v sin θ) t, y = (v cos θ) t + (1/2)gt^2

31. If two projectiles are launched with the same initial speed but at complementary angles (e.g., 30° and 60°), their ranges will be:

A) Different B) Same C) Zero D) Double

32. A bird flies with a velocity of 15 m/s in still air. The wind is blowing at 5 m/s due East. If the bird flies in the North direction relative to the ground, its velocity relative to the air must be:

A) 15 m/s North B) 20 m/s North C) 10 m/s North D) sqrt(200) m/s North

33. Consider a particle moving in a circle of radius r with constant speed v. Its acceleration is always directed towards the center and its magnitude is:

A) v/r B) v^2/r C) vr D) v/r^2

34. If a projectile is launched horizontally from a height h, the time taken to reach the ground is the same as the time taken for a body to fall freely from height h. This is because:

A) Horizontal and vertical motions are independent B) Gravity affects horizontal motion C) Initial horizontal velocity is zero D) Air resistance is ignored

35. The maximum height reached by a projectile launched at an angle of 45 degrees is H. What will be the maximum height if the launch angle is 30 degrees with the same initial speed?

A) H/2 B) 3H/4 C) H/4 D) 2H

36. A vector A has magnitude 5 units and makes an angle of 37 degrees with the positive x-axis. Its x-component is approximately:

A) 3 units B) 4 units C) 2.5 units D) 5 units

37. If the resultant velocity of a boat in a river is perpendicular to the river flow, and the velocity of the river is v_r, and the velocity of the boat relative to water is v_b, then v_b must be:

A) Equal to v_r B) Greater than v_r C) Less than v_r D) Zero

38. In projectile motion, the acceleration vector is:

A) Zero B) Constant and directed downwards C) Variable and depends on velocity D) Tangential to the trajectory

39. What is the unit vector in the direction of vector A = 3i + 4j?

A) (3i + 4j)/5 B) (3i + 4j)/7 C) (3i + 4j)/12 D) 3i + 4j

40. If a particle is moving in a plane such that its velocity components are v_x = 2 m/s and v_y = 3 m/s, its resultant velocity is:

A) 5 m/s B) sqrt(5) m/s C) sqrt(13) m/s D) 6 m/s

41. The angle of projection for maximum range is:

A) 0° B) 30° C) 45° D) 60°

42. If a projectile is launched with initial velocity v and hits the target at the same horizontal level, the launch angle for maximum height is:

A) 0° B) 30° C) 45° D) 90°

43. The time of flight for a projectile launched horizontally from height h is:

A) sqrt(h/g) B) sqrt(2h/g) C) 2h/g D) sqrt(gh)

44. A vector A = 2i - 3j + k. What is the magnitude of A?

A) sqrt(14) B) sqrt(10) C) sqrt(12) D) sqrt(6)

45. Two vectors are parallel if their cross product is:

A) Zero B) Maximum C) Equal to their dot product D) Minimum

46. A plane flies with a speed of 200 km/h relative to the air. The wind is blowing from the west at 50 km/h. To fly due north, the pilot must steer the plane at an angle of approximately:

A) 15° West of North B) 15° East of North C) 75° West of North D) 75° East of North

47. In projectile motion, the quantity that remains constant throughout the flight (neglecting air resistance) is:

A) Velocity B) Speed C) Horizontal component of velocity D) Vertical component of velocity

48. If a projectile is launched with speed v at angle θ, and another projectile is launched with speed v at angle (90°-θ), the ratio of their maximum heights will be:

A) sin^2 θ : cos^2 θ B) cos^2 θ : sin^2 θ C) tan^2 θ : cot^2 θ D) cot^2 θ : tan^2 θ

49. A boat moves across a river with velocity 4 m/s relative to the water. The river flows with velocity 3 m/s. If the boat wants to reach the point directly opposite to its starting point, it must aim upstream at an angle θ such that:

A) tan θ = 3/4 B) tan θ = 4/3 C) sin θ = 3/4 D) cos θ = 3/4

50. The horizontal range of a projectile is maximum when the angle of projection is:

A) 30° B) 45° C) 60° D) 90°

Resolution of a vector, relative velocity, motion in a plane, projectile motion - Online Test

Test Results