Class 11 Physics MCQ Assignment: Motion in a Plane
1. Which of the following is a scalar quantity?
Hint: Look for the quantity that does not require directional specification.
Answer: C
2. Two vectors are perpendicular to each other if their:
Hint: Think about the trigonometric identity where cosine of 90 degrees equals zero.
Answer: B
3. What is the angle of projection for a projectile to achieve maximum horizontal range?
Hint: The range formula involves sin(2θ). For maximum value, sin(2θ) must equal 1.
Answer: B
4. A particle moves in a circle of radius r with a constant speed v. The acceleration of the particle is:
Hint: This is uniform circular motion. Recall centripetal acceleration.
Answer: C
5. The path followed by a projectile is called its:
Hint: It forms a parabolic curvature shape in two dimensions.
Answer: B
6. If the horizontal and vertical components of a vector are equal, the angle made by the vector with the horizontal is:
Hint: tan(θ) = Vertical component / Horizontal component.
Answer: B
7. A car turns a sharp corner at a constant speed. What is the direction of the net force acting on the car during the turn?
Hint: Consider the static friction acting as the necessary centripetal force.
Answer: B
8. The cross product of two parallel vectors is:
Hint: Magnitude of cross product depends on sin(θ). For parallel vectors, θ = 0°.
Answer: B
9. At the highest point of a projectile's trajectory, its velocity and acceleration are:
Hint: Velocity is strictly horizontal at the top, while acceleration due to gravity acts vertically downwards.
Answer: B
10. The horizontal component of velocity of a projectile remains constant throughout because:
Hint: Think about Newton's first law and the direction of gravitational force.
Answer: D
11. What is the unit vector perpendicular to the vectors A = i and B = j?
Hint: Use the right-hand cyclic thumb rule for unit vectors cross product.
Answer: C
12. The magnitude of the sum of two vectors A and B is given by:
Hint: Apply the law of parallelograms of vector addition.
Answer: C
13. For any non-zero vector A, the expression A • A is equal to:
Hint: The angle between a vector and itself is 0°. cos(0°) = 1.
Answer: C
14. If the velocity of a particle is given by v = (2i + 3jt) m/s, the acceleration of the particle is:
Hint: Take the derivative of the velocity equation with respect to time (dv/dt).
Answer: C
15. A stone is dropped from a running bus. The path followed by the stone as observed by a person standing on the ground is:
Hint: The stone possesses initial horizontal speed of the bus but falls freely under gravity.
Answer: C
16. The angular speed of a minute hand of a clock is:
Hint: ω = 2π / T. A minute hand completes one revolution in 60 minutes. Convert minutes to seconds.
Answer: A
17. A position vector is defined as:
Hint: It specifies the coordinates of a particle relative to a reference origin point.
Answer: B
18. If the time of flight of a projectile is doubled, its maximum height attained becomes:
Hint: T ∝ sinθ and H ∝ sin²θ, so H is directly proportional to T².
Answer: B
19. Which of the following ranges matches the angle of projection 15° for the same initial velocity?
Hint: Projectiles projected at complementary angles (θ and 90° - θ) have the same range.
Answer: C
20. In non-uniform circular motion, the net acceleration vector is:
Hint: Both speed changes and direction changes occur concurrently.
Answer: C
21. The property of vector addition that states A + B = B + A is called:
Hint: Order of operation modification does not change final vector result value.
Answer: B
22. What is the dot product of two mutually perpendicular unit vectors i and j?
Hint: cos(90°) parameters control this result value completely.
Answer: B
23. A boat is sent across a river with a velocity of 8 km/h. If the river flows at 6 km/h, the resultant velocity of the boat is:
Hint: The velocity values are perpendicular. Use Pythagoras theorem formula: √(8² + 6²).
Answer: C
24. The maximum horizontal range of a projectile is 400 m. What is its maximum height achieved?
Hint: At θ = 45° (for max range), H_max = R_max / 4.
Answer: A
25. If three vectors are coplanar, it implies that:
Hint: Review mathematical definitions of geometric planes and vector volumes.
Answer: D
26. A vector which has zero magnitude and an arbitrary direction is termed as:
Hint: It acts as the additive identity element in vector mathematics.
Answer: B
27. An object is moving with constant acceleration in two dimensions. Its trajectory could be a:
Hint: Think about projectile motion (parabola) or standard linear motion accelerated consistently.
Answer: D
28. The linear velocity vector equals the cross product of:
Hint: The structural vector relation formula is v = ω × r.
Answer: A
29. If the dot product of two non-zero vectors equals the magnitude of their cross product, the angle between them is:
Hint: AB cosθ = AB sinθ. Determine where sinθ = cosθ.
Answer: B
30. Centripetal force acts towards:
Hint: The word 'centripetal' itself translates literally to 'center-seeking'.
Answer: A
31. What is the magnitude of vector A = 3i + 4j?
Hint: Solve using standard formula |A| = √(Ax² + Ay²).
Answer: B
32. The range of a projectile depends on:
Hint: Examine the analytical algebraic structure of the Range equation: R = u²sin(2θ)/g.
Answer: D
33. If an object completes 2 revolutions per second in a circle, its frequency in Hz is:
Hint: Frequency is explicitly defined as the number of full complete cycles executed per unit second.
Answer: B
34. Unit vectors are used explicitly to define:
Hint: Their magnitude value is strictly fixed to unity (one) without carrying metrics or dimensions.
Answer: B
35. A projectile is thrown with initial velocity u making angle θ with horizontal. The velocity vector at any time t is:
Hint: Separate components. Horizontal remains unchanged; vertical uses v_y = u_y - gt.
Answer: A
36. Rain is falling vertically down at 4 m/s. A man walks horizontally at 3 m/s. The velocity of rain relative to man is:
Hint: v_rm = √(v_r² + v_m²). Apply perpendicular relative velocity summation mechanics.
Answer: C
37. The displacement of a particle moving in a circular path of radius R after completing a half cycle is:
Hint: Displacement is the absolute shortest straight line distance between initial and final locations.
Answer: B
38. Resolution of a vector means:
Hint: It is the inverse reverse process operation of vector addition.
Answer: B
39. Two projectiles are projected with same speed at 30° and 60° respectively. The ratio of their maximum heights is:
Hint: Height depends on sin²θ. Compute the ratio of sin²(30°) to sin²(60°).
Answer: A
40. The relation between linear acceleration 'a' and angular acceleration 'α' in a circle of radius r is:
Hint: Recall how linear arc length metrics relate back to angular dimensions via radius transformations.
Answer: B
41. What is the maximum number of rectangular components a vector can be resolved into in a three-dimensional space?
Hint: Think about the total number of mutually perpendicular independent spatial axes (x, y, z).
Answer: B
42. The time of flight of a projectile is given by the formula:
Hint: Total flight duration is twice the time required to climb to maximum peak height.
Answer: B
43. When a particle completes one full cycle of uniform circular motion, its average velocity is:
Hint: Average velocity is defined strictly as Net Displacement divided by Total Time.
Answer: B
44. The acceleration vector of a projectile during its motion is:
Hint: The only force acting throughout is gravity, which pulls downwards continuously at 9.8 m/s².
Answer: C
45. If vector A = 2i + j and vector B = i - 2j, then their dot product A • B is:
Hint: Calculate values via corresponding components: (Ax * Bx) + (Ay * By).
Answer: B
46. A swimmer can swim in still water at 5 m/s. He wants to cross a river flowing at 3 m/s in the shortest time path. He must swim at what angle to the flow line?
Hint: To achieve minimum crossing duration time, maximize velocity strictly directed across the width.
Answer: A
47. The trajectory equation of a standard projectile path is expressed analytically as:
Hint: Eliminate the time parameter variable 't' by substituting t = x / (u cosθ) into vertical displacement kinematics.
Answer: A
48. The magnitude of displacement vector of a particle moving from coordinate position (1,2) to (4,6) is:
Hint: Determine changes first: Δx = 4-1=3, Δy = 6-2=4. Then apply √(Δx² + Δy²).
Answer: B
49. Uniform circular motion is an example of an accelerated motion with:
Hint: The value v²/r remains unchanged, but its directional arrow rotates with the particle position.
Answer: A
50. Can the resultant of two unequal non-zero vectors be a null vector?
Hint: To cancel out completely to zero, opposing vectors must possess perfectly equal opposite magnitudes.
Answer: B