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1. A quantity having both magnitude and direction is called a:
A. Vector quantity
B. Scalar quantity
C. Dimensionless quantity
D. Base quantity
Answer: A. Vector quantity
Explanation: Vector quantities, unlike scalars, require both a magnitude and a specific direction to be fully described.
2. A quantity having only magnitude and no direction is called a:
A. Scalar quantity
B. Vector quantity
C. Position vector
D. Null vector
Answer: A. Scalar quantity
Explanation: Scalar quantities are completely described by their magnitude alone, without any associated direction.
3. The method of adding vectors by placing the tail of one vector at the head of another is called the:
A. Triangle law of vector addition
B. Scalar multiplication method
C. Dot product method
D. Cross product method
Answer: A. Triangle law of vector addition
Explanation: The triangle law of vector addition involves joining vectors head-to-tail, with the resultant drawn from the start of the first to the end of the second.
4. The method of adding two vectors represented as adjacent sides of a figure is called the:
A. Parallelogram law of vector addition
B. Triangle law only
C. Polygon method exclusively
D. Scalar addition method
Answer: A. Parallelogram law of vector addition
Explanation: The parallelogram law states that if two vectors are represented as adjacent sides of a parallelogram, their sum is given by the diagonal from the common point.
5. A vector with zero magnitude is called a:
A. Null vector
B. Unit vector
C. Position vector
D. Resultant vector
Answer: A. Null vector
Explanation: A null (or zero) vector has zero magnitude and an arbitrary or undefined direction.
6. A vector with magnitude equal to one is called a:
A. Unit vector
B. Null vector
C. Scalar vector
D. Position vector
Answer: A. Unit vector
Explanation: A unit vector is specifically defined as having a magnitude of exactly one, often used to indicate direction only.
7. The horizontal and vertical components of a vector are called its:
A. Rectangular components
B. Scalar components only
C. Null components
D. Unit components
Answer: A. Rectangular components
Explanation: Rectangular components refer to the perpendicular (typically horizontal and vertical) parts into which a vector can be resolved.
8. The path followed by a projectile under the influence of gravity alone is called:
A. A parabola
B. A straight line
C. A circle
D. An ellipse
Answer: A. A parabola
Explanation: Neglecting air resistance, the trajectory of a projectile launched at an angle follows a parabolic path due to gravity.
9. The maximum height attained by a projectile depends on:
A. The vertical component of its initial velocity
B. The horizontal component of its initial velocity only
C. Only the total time of flight
D. The mass of the projectile
Answer: A. The vertical component of its initial velocity
Explanation: Maximum height in projectile motion is determined by the vertical component of the initial velocity, since gravity acts only vertically.
10. The horizontal range of a projectile is maximum when the angle of projection is:
A. 45°
B. 90°
C. 0°
D. 30°
Answer: A. 45°
Explanation: For a given initial speed, the horizontal range of a projectile is maximised when it is launched at an angle of 45° to the horizontal.
11. In uniform circular motion, the speed of the object remains:
A. Constant
B. Continuously increasing
C. Continuously decreasing
D. Zero
Answer: A. Constant
Explanation: In uniform circular motion, while the direction of velocity changes constantly, the magnitude (speed) remains constant.
12. In uniform circular motion, the acceleration is directed:
A. Towards the centre of the circular path
B. Away from the centre
C. Along the tangent to the path
D. In a fixed, unchanging direction
Answer: A. Towards the centre of the circular path
Explanation: This acceleration, known as centripetal acceleration, always points towards the centre of the circular path.
13. The acceleration responsible for uniform circular motion is called:
A. Centripetal acceleration
B. Tangential acceleration
C. Gravitational acceleration only
D. Angular acceleration only
Answer: A. Centripetal acceleration
Explanation: Centripetal acceleration is the specific term used for the inward-directed acceleration causing circular motion.
14. The formula for centripetal acceleration in terms of velocity (v) and radius (r) is:
A. v²/r
B. vr
C. v/r²
D. v²r
Answer: A. v²/r
Explanation: Centripetal acceleration is calculated as the square of the velocity divided by the radius of the circular path.
15. Scalar multiplication of a vector by a negative number results in a vector that is:
A. Reversed in direction
B. Unchanged in direction
C. Always zero
D. Rotated by 90°
Answer: A. Reversed in direction
Explanation: Multiplying a vector by a negative scalar reverses its direction while scaling its magnitude according to the absolute value of the scalar.
16. The angle of projection that gives equal maximum height and horizontal range is related through:
A. A specific mathematical relationship involving the tangent of the angle
B. Always 90°
C. Always 0°
D. No definable relationship
Answer: A. A specific mathematical relationship involving the tangent of the angle
Explanation: There exists a specific angle at which the maximum height equals the horizontal range, derivable using projectile motion equations involving tan of the angle.
17. The time of flight of a projectile depends primarily on:
A. The vertical component of the initial velocity
B. The horizontal component of the initial velocity only
C. The mass of the object
D. The colour of the object
Answer: A. The vertical component of the initial velocity
Explanation: Since gravity acts vertically, the time the projectile remains in the air is governed by the vertical component of its initial velocity.
18. Which of the following is an example of a vector quantity?
A. Displacement
B. Mass
C. Time
D. Temperature
Answer: A. Displacement
Explanation: Displacement, having both magnitude and direction, is a vector quantity, unlike mass, time or temperature which are scalars.
19. Which of the following is an example of a scalar quantity?
A. Speed
B. Velocity
C. Acceleration
D. Force
Answer: A. Speed
Explanation: Speed only has magnitude and no direction, making it a scalar quantity, unlike velocity, acceleration and force.
20. The resultant of two vectors acting in the same direction is found by:
A. Adding their magnitudes directly
B. Subtracting their magnitudes
C. Multiplying their magnitudes
D. Taking their average
Answer: A. Adding their magnitudes directly
Explanation: When two vectors point in exactly the same direction, their resultant magnitude is simply the sum of their individual magnitudes.
21. The resultant of two vectors acting in exactly opposite directions is found by:
A. Subtracting the smaller magnitude from the larger
B. Adding their magnitudes
C. Multiplying their magnitudes
D. Ignoring both vectors
Answer: A. Subtracting the smaller magnitude from the larger
Explanation: When vectors point in opposite directions, the resultant magnitude equals the difference between their magnitudes, directed along the larger vector.
22. The angular displacement in circular motion is measured in units of:
A. Radians
B. Metres
C. Seconds
D. Newtons
Answer: A. Radians
Explanation: Angular displacement, describing rotational motion, is conventionally measured in radians (or sometimes degrees).
23. The relationship between linear velocity (v), angular velocity (ω) and radius (r) in circular motion is given by:
A. v = ωr
B. v = ω/r
C. v = ω + r
D. v = ω - r
Answer: A. v = ωr
Explanation: This fundamental relation connects linear speed to angular speed, scaled by the radius of the circular path.
24. A projectile launched horizontally from a height will follow a path that is:
A. Parabolic, combining constant horizontal velocity and accelerating vertical motion
B. A straight vertical line
C. A perfect circle
D. A straight horizontal line
Answer: A. Parabolic, combining constant horizontal velocity and accelerating vertical motion
Explanation: Since horizontal velocity remains constant while vertical velocity increases due to gravity, the combined path traces a parabola.
25. For projectile motion, air resistance is typically:
A. Neglected in basic calculations for simplicity
B. Always the dominant factor considered
C. Equal to gravitational force
D. Impossible to ignore in any scenario
Answer: A. Neglected in basic calculations for simplicity
Explanation: In introductory projectile motion problems, air resistance is generally neglected to simplify the mathematical analysis.
26. The dot product (scalar product) of two perpendicular vectors is:
A. Zero
B. Equal to the product of their magnitudes
C. Always negative
D. Always equal to one
Answer: A. Zero
Explanation: Since the cosine of 90° is zero, the dot product of two mutually perpendicular vectors always evaluates to zero.
27. The cross product (vector product) of two parallel vectors is:
A. A null vector
B. Maximum in magnitude
C. Equal to their dot product
D. Undefined
Answer: A. A null vector
Explanation: Since the sine of 0° (the angle between parallel vectors) is zero, their cross product results in a null vector.
28. In vector addition, the resultant vector's magnitude depends on both the magnitudes of the individual vectors and the:
A. Angle between them
B. Colour of the vectors
C. Their scalar components only
D. Time taken
Answer: A. Angle between them
Explanation: The magnitude of the resultant vector, calculated using the parallelogram or triangle law, depends critically on the angle separating the two original vectors.
29. The horizontal component of a projectile's velocity throughout its flight (ignoring air resistance) remains:
A. Constant
B. Continuously increasing
C. Continuously decreasing
D. Zero throughout
Answer: A. Constant
Explanation: Since gravity acts only vertically, the horizontal component of velocity is unaffected and remains constant throughout the flight.
30. The vertical component of a projectile's velocity changes due to:
A. The constant downward acceleration due to gravity
B. Air resistance being the primary factor
C. The horizontal velocity component
D. The projectile's colour
Answer: A. The constant downward acceleration due to gravity
Explanation: Gravity continuously acts downward on the projectile, steadily changing (decreasing then increasing in magnitude) its vertical velocity component.
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