Motion in a Plane – Scalars and Vectors - UNSOLVED PRACTICE SET
Chapter: Kinematics | Topic: Motion in a Plane Scalars and Vectors
MOTION IN A PLANE – SCALARS AND VECTORS - UNSOLVED PRACTICE SET
Topic: Motion in a Plane Scalars and Vectors
Multiple Choice Questions
Q1. Which of the following is a vector quantity?
- Mass
- Temperature
- Velocity
- Time
Q2. Two vectors are equal if:
- They have the same magnitude only
- They have the same direction only
- They have the same magnitude and the same direction
- They act on the same body
Q3. The negative of a vector A is a vector:
- With the same magnitude but opposite direction
- With the same magnitude and same direction
- With double the magnitude
- With half the magnitude
Q4. Which of the following operations is NOT valid for vectors?
- Addition
- Subtraction
- Division by another vector
- Multiplication by a scalar
Q5. A vector multiplied by a negative scalar:
- Changes only its magnitude
- Changes only its direction
- Changes both magnitude and direction
- Remains unchanged
Q6. The position vector of a point P(x, y) with respect to the origin is:
- xi + yj
- x + y
- √(x² + y²)
- x − y
Short Answer Questions
Q7. Distinguish between scalar and vector quantities. Give two examples of each.
Q8. Define a null vector and a unit vector. Give one example of where each is used in physics.
Q9. If vector A = 3i + 4j, find:
(a) The magnitude of A
(b) The unit vector in the direction of A
Q10. In your school playground, a student walks 40 m east and then 30 m north. Represent this displacement as a vector and calculate its magnitude and direction.
Q11. Two vectors A and B have magnitudes 5 units and 12 units respectively. What are the maximum and minimum possible magnitudes of their resultant?
Q12. A vector A makes an angle of 30° with the positive x-axis and has a magnitude of 10 units. Find its rectangular components.
Long Answer Questions
Q13. Explain the concept of vectors and scalars with examples. Discuss the properties of vectors including:
(i) Equality of vectors
(ii) Negative of a vector
(iii) Multiplication of a vector by a real number
(iv) Position vectors and displacement vectors
Illustrate each property with a diagram or example.
Q14. Three vectors A, B, and C have magnitudes 3 units, 4 units, and 5 units respectively. Vector A is along the positive x-axis, Vector B is at 60° to the positive x-axis, and Vector C is at 120° to the positive x-axis.
(a) Express each vector in component form.
(b) Calculate the resultant of A + B + C.
(c) Find the magnitude and direction of the resultant.
Q15. A physics teacher asks students to perform a "Vector Walk" in the school ground. Student P walks 100 m at 30° north of east. Student Q walks 100 m at 30° south of east. Student R walks 100 m east and then 100 m north.
(a) Represent each student's walk using vectors.
(b) Calculate the displacement of each student from the starting point.
(c) Compare the magnitudes of their displacements.
(d) What does this activity teach about vectors and their addition?
Application-Based Problems
Q16. A bird flies 5 km east, then 3 km north, then 2 km west, and finally 4 km south.
(a) Represent each displacement as a vector in component form.
(b) Calculate the resultant displacement vector.
(c) Find the magnitude and direction of the resultant displacement.
(d) Calculate the total path length and compare it with the magnitude of displacement.
Q17. Two forces F₁ = 10 N and F₂ = 15 N act on a body at the origin. F₁ acts along the positive x-axis and F₂ acts at 60° to the positive x-axis.
(a) Express both forces in vector component form.
(b) Calculate the resultant force.
(c) Find the magnitude and direction of the resultant force.
(d) A third force F₃ is to be applied so that the net force on the body is zero. Find F₃ in component form.Q. Type your question here...
Q18. In a navigation exercise, a ship sails 20 km at 45° north of east, then 15 km at 30° south of east, and finally 25 km due north.
(a) Draw a vector diagram representing the journey.
(b) Calculate the final position vector of the ship relative to the starting point.
(c) Calculate the straight-line distance from the starting point to the final position.
(d) Calculate the direction of the final displacement from the starting point.