Class 11 Physics — Chapter 4: Motion in a Plane Online Test

1. If the frequency of a wheel is 10 Hz, what is its period?

2. Which relation connects period T, frequency f, and angular velocity ω?

3. A projectile is launched at angle onto a plane inclined at . Which relation gives its range along the plane?

4. In the same case, what is the range measured along the inclined plane?

5. Which statement is correct regarding the horizontal component of velocity in projectile motion (neglecting air resistance)?

6. If object A has velocity and object B has velocity , then magnitude of is:

7. If and , then equals:

8. A projectile is fired at 20 m/s horizontally from a cliff 45 m high. Find the time it takes to hit the ground. (g = 10 m/s²)

9. If a particle has initial velocity and constant acceleration , what is its velocity after 5 seconds?

10. A body moves in a plane with constant acceleration . If initial velocity is zero, what is the displacement after 4 s?

11. For the same projectile, what is the y-coordinate after time ?

12. The trajectory of a projectile is given by:

13. A satellite of mass m revolves around Earth in a circular orbit of radius r with speed v. The centripetal force is provided by gravity. Which equation represents this balance?

14. In projectile motion, why is the trajectory parabolic instead of linear?

15. Which of the following best illustrates why two-dimensional motion must be studied separately from one-dimensional motion?

16. Heat energy is considered a scalar because:

17. If a displacement vector has components m and m, what is its magnitude?

18. A vector has components and . What angle does it make with the x-axis?

19. If , what is the magnitude of ?

20. Multiplying a vector by a scalar :

1. The resultant of two vectors and is:

2. A projectile is launched from a 60 m high cliff with speed 30 m/s at 40° above the horizontal. Neglecting air resistance, what is the horizontal range from the foot of the cliff? (g = 9.8 m/s²)

3. The time taken for one complete revolution in circular motion is called:

4. A bullet moves with velocity 200 m/s and strikes a target making an angle of with the horizontal. Find its horizontal component of velocity.

5. What is the relation between and ?

6. A particle starts from rest and accelerates at . Find its displacement after 2 seconds.

7. What is the shape of the trajectory of a projectile (neglecting air resistance)?

8. The direction of a vector in a plane is measured with respect to:

9. For a given velocity, what is the angle of projection that produces maximum range?

10. Point B is 300 m east and 200 m north of point A across a river. Current is 3 m/s east; a boat can do 5 m/s in still water. At what heading (east of north) should the boat aim to go straight to B in the shortest time, and what is that time?

11. A body moves in a circle of radius 2 m with speed 6 m/s. Find its centripetal force if its mass is 3 kg.

12. Why is speed considered a scalar while velocity is not?

13. Which statement is correct about the effect of multiplying a vector by zero?

14. A car accelerates uniformly from rest along x with . Find displacement after 5 s.

15. A force of 100 N acts at an angle of with the horizontal. What is the horizontal component of this force?

16. Why is velocity considered a vector while speed is a scalar?

17. A force of is applied at an angle of above the horizontal. What is its vertical component?

18. If two vectors and , their resultant is:

19. Car A moves with velocity east and Car B moves with velocity north. What is the velocity of A relative to B?

20. Why does a body moving in a circle require centripetal acceleration?

21. A projectile is fired at 20 m/s horizontally from a cliff 45 m high. Find the time it takes to hit the ground. (g = 10 m/s²)

22. Which of the following is an example of a vector quantity?

23. A projectile is fired with initial speed 40 m/s at angle 30°. Find its horizontal range. (g = 10 m/s²)

24. A car travels 60 km/h towards the north. Which statement best describes this?

25. Which quantity remains constant throughout projectile motion?

26. A target initially at (200 m, 0) moves left at 10 m/s. A projectile is launched from the origin at speed 60 m/s to intercept the target at the same level (air resistance neglected). What launch angle should be used? (g = 9.8 m/s²)

27. A displacement vector of 6 km east is multiplied by -1. Geometrically, the new vector represents:

28. A car travels east 40 km and then north 30 km. Why do we need two-dimensional motion analysis here?

29. A car moves east and then north. Using analytical vector addition, what is the resultant displacement?

30. Which statement is correct about acceleration in two dimensions?

1. A train increases its velocity from 10 m/s to 30 m/s in 10 seconds along a straight line. Its acceleration is:

2. A planet of mass m revolves around the Sun at distance r with orbital period T. Which relation holds true?

3. Which of the following statements is correct about centripetal acceleration?

4. If two equal vectors of magnitude are inclined at angle , their resultant magnitude by parallelogram law is:

5. If a displacement vector of 10 m north is multiplied by -3, the new vector is:

6. A particle moves in a circle of radius 0.50 m. Its speed increases uniformly from 0 to 20 m/s in 5 s. What is the magnitude of its acceleration at s?

7. A particle starts from rest and moves with constant acceleration in a plane. After 5 s it is at (90 m, 120 m) and its speed is 60 m/s. What is the acceleration vector?

8. The trajectory equation of a projectile can be compared to a parabola of the form:

9. If two vectors of 6 N and 8 N act at right angles, the resultant according to parallelogram law is:

10. Plane flies with km/h relative to air. Wind velocity is km/h north. Find velocity of plane relative to ground.

11. Multiplying a vector by a negative scalar results in:

12. A vector has components and . Write its analytical representation.

13. A displacement vector of 6 km east is multiplied by -1. Geometrically, the new vector represents:

14. Why is velocity considered a vector while speed is a scalar?

15. In the parallelogram method, if two vectors and are at right angles, then the magnitude of the resultant is:

16. A runner completes one full lap of 400 m around a circular track. Which quantity is scalar?

17. Which of the following is not a scalar quantity?

18. Which one of the following is a scalar quantity?

19. A displacement vector is represented in Cartesian coordinates as . Its magnitude and direction angle are:

20. A boat (speed 6 m/s in still water) must cross a 240 m wide river with current 3 m/s east. If the boat heads straight across (minimum-time strategy), what are the crossing time and downstream drift?

21. If vector has magnitude , then magnitude of is:

22. If a vector has components and , then its magnitude is:

23. An airplane taking a curved turn in the sky is an example of:

24. A man walks 4 km east and then 3 km north. Using analytical vector addition, find displacement.

25. Which formula gives the velocity magnitude of a projectile at time ?

26. Which physical quantity changes continuously in uniform circular motion?

27. Which of the following is an example of a scalar quantity?

28. For the same projectile, what is the y-coordinate after time ?

29. The study of two-dimensional motion mainly requires the use of:

30. A force of 100 N acts at an angle of with the horizontal. Using geometric resolution, the vertical component is:

31. A target 150 m due east moves due north at 10 m/s. A projectile is fired from the origin at speed 100 m/s (neglect gravity for the short flight). At what yaw angle to the east (towards the north) should it be aimed to hit the target?

32. If and , then graphically is:

33. Which scenario is an example of projectile motion (neglecting air resistance)?

34. A projectile has a range of 80 m when launched at 30° with velocity u. If launched at 60° with the same velocity, what will be the range?

35. Two projectiles are fired with the same speed u at angles θ and (90° − θ). Which statement is true (same level launch/landing)?

36. A particle moves on a circle of radius 3.0 m with angular acceleration rad/s^2 from rad/s. What is the total acceleration magnitude at s?

37. Why does the effective acceleration along an inclined plane appear as ?

38. A vector of magnitude 15 units is inclined at with the x-axis. Find its horizontal component.

39. If a vector of magnitude 12 units is multiplied by scalar 4, what will be the magnitude of the new vector?

40. A vector makes an angle of with the horizontal and has a magnitude of 14 N. What is the value of its vertical component?

41. A projectile is fired at 50 m/s at an angle of 45°. Find its time of flight. (g = 10 m/s²)

42. An airplane flies with velocity east, while wind blows at north. Find the resultant velocity using analytical addition.

43. Why is projectile motion on an inclined plane more complex than on horizontal ground?

44. If an object moves along a curved path with varying direction, the motion is called:

45. The mathematical equation of a projectile trajectory is:

46. A projectile is launched from a 60 m high cliff with speed 30 m/s at 40° above the horizontal. Neglecting air resistance, what is the horizontal range from the foot of the cliff? (g = 9.8 m/s²)

47. A cyclist rides north at 10 m/s. The wind blows such that rain appears vertical to him. If real rain velocity is 10 m/s vertical downward, what is the wind velocity?

48. A projectile must just clear the top of a hill located 60 m away and 25 m high when fired at 45°. What is the minimum launch speed? (g = 9.8 m/s²)

49. If two vectors of equal magnitude act in opposite directions, the result of their subtraction graphically is:

50. From level ground, the projectile must pass exactly through the point . What is the minimum launch speed (choose the best angle)? Use m/s^2.