Scalar And Vector MCQ Quiz With Answers

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

Temperature

Velocity

Volume

Mass

Velocity is an example of a vector quantity because it has both magnitude and direction. In physics, vectors are quantities that require both a numerical value and a specific direction to fully describe them. Velocity, specifically, represents the rate at which an object changes its position and includes information about the object's speed as well as the direction it is moving in. Therefore, velocity satisfies the criteria of a vector quantity.

Explanation

Velocity is an example of a vector quantity because it has both magnitude and direction. In physics, vectors are quantities that require both a numerical value and a specific direction to fully describe them. Velocity, specifically, represents the rate at which an object changes its position and includes information about the object's speed as well as the direction it is moving in. Therefore, velocity satisfies the criteria of a vector quantity.

2. Which of the following is a physical quantity that has both magnitude and direction?

Vector

Scalar

Frame of reference

Resultant

A vector is a physical quantity that has both magnitude and direction. It represents quantities such as displacement, velocity, and force. Magnitude refers to the size or quantity of the vector, while direction indicates its orientation in space. Unlike scalars, which only have magnitude, vectors require both magnitude and direction to completely describe them. A frame of reference is a coordinate system used to describe the position and motion of objects, while a resultant is the sum or combination of multiple vectors. However, only a vector possesses both magnitude and direction.

Explanation

A vector is a physical quantity that has both magnitude and direction. It represents quantities such as displacement, velocity, and force. Magnitude refers to the size or quantity of the vector, while direction indicates its orientation in space. Unlike scalars, which only have magnitude, vectors require both magnitude and direction to completely describe them. A frame of reference is a coordinate system used to describe the position and motion of objects, while a resultant is the sum or combination of multiple vectors. However, only a vector possesses both magnitude and direction.

3. Which of the following is a physical quantity that has a magnitude but no direction?

Vector

Frame of reference

Resultant

Scalar

A scalar is a physical quantity that only has a magnitude, meaning it can be described by a numerical value alone without any reference to direction. Unlike vectors, which have both magnitude and direction, scalars represent quantities such as mass, temperature, or time that do not have a specific orientation or direction associated with them. Therefore, the correct answer is scalar.

Explanation

A scalar is a physical quantity that only has a magnitude, meaning it can be described by a numerical value alone without any reference to direction. Unlike vectors, which have both magnitude and direction, scalars represent quantities such as mass, temperature, or time that do not have a specific orientation or direction associated with them. Therefore, the correct answer is scalar.

4. What type of quantity is mass when it is measured as 5 kilograms?

Scalar

Vector

Vector when in motion

Both scalar and vector

Mass is a scalar quantity. Scalar quantities have magnitude (amount) only and no direction. In the case of mass, whether an object is stationary or in motion, its mass remains the same, and it is measured in kilograms (kg). Vector quantities, on the other hand, have both magnitude and direction (e.g., force, velocity). Mass does not have a direction associated with it, so it is classified as a scalar quantity. Therefore, the correct answer is A) Scalar.

Explanation

Mass is a scalar quantity. Scalar quantities have magnitude (amount) only and no direction. In the case of mass, whether an object is stationary or in motion, its mass remains the same, and it is measured in kilograms (kg). Vector quantities, on the other hand, have both magnitude and direction (e.g., force, velocity). Mass does not have a direction associated with it, so it is classified as a scalar quantity. Therefore, the correct answer is A) Scalar.

5. What kind of physical quantity is a force of 10 Newtons applied to push a box to the right?

Scalar

Vector

Unitless

Dimensionless

A force of 10 Newtons applied to push a box to the right is classified as a vector quantity. Vectors have both magnitude and direction. In this case, the magnitude of the force is 10 Newtons, and the direction is to the right. Scalars, in contrast, have only magnitude and no direction (e.g., temperature, mass). Unitless and dimensionless quantities lack units or dimensions and are typically used for pure numbers or ratios. Therefore, the correct answer is B) Vector.

Explanation

A force of 10 Newtons applied to push a box to the right is classified as a vector quantity. Vectors have both magnitude and direction. In this case, the magnitude of the force is 10 Newtons, and the direction is to the right. Scalars, in contrast, have only magnitude and no direction (e.g., temperature, mass). Unitless and dimensionless quantities lack units or dimensions and are typically used for pure numbers or ratios. Therefore, the correct answer is B) Vector.

6. Identify the following quantities as scalar or vector: the mass of an object, the number of leaves on a tree, and wind velocity.

Vector, scalar, scalar

Vector, scalar, vector

Scalar, scalar, vector

Scalar, vector, vector

The mass of an object is a scalar quantity because it only has magnitude and no direction. The number of leaves on a tree is also a scalar quantity as it only represents a count and does not have any direction associated with it. Wind velocity, on the other hand, is a vector quantity because it has both magnitude (speed) and direction (the direction in which the wind is blowing).

Explanation

The mass of an object is a scalar quantity because it only has magnitude and no direction. The number of leaves on a tree is also a scalar quantity as it only represents a count and does not have any direction associated with it. Wind velocity, on the other hand, is a vector quantity because it has both magnitude (speed) and direction (the direction in which the wind is blowing).

7. Which trigonometric function, when multiplied by a vector's magnitude, gives the x-component of a vector oriented at an angle with respect to the x-axis in a coordinate system?

Tan θ

Cos θ

Cot θ

Sin θ

In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its x-component can be found using the cosine function. The x-component (V_x) is equal to the vector's magnitude (V) multiplied by the cosine of the angle (θ):

V_x=V cosθ

This relationship comes from the definition of the cosine function in a right triangle, where the adjacent side (x-component) is equal to the hypotenuse (vector's magnitude) multiplied by the cosine of the angle. This is a fundamental concept in vector decomposition.

Explanation

In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its x-component can be found using the cosine function. The x-component (V_x) is equal to the vector's magnitude (V) multiplied by the cosine of the angle (θ):

V_x=V cosθ

This relationship comes from the definition of the cosine function in a right triangle, where the adjacent side (x-component) is equal to the hypotenuse (vector's magnitude) multiplied by the cosine of the angle. This is a fundamental concept in vector decomposition.

8. Which of the following is not an example of projectile motion?

A volleyball served over a net.

A baseball thrown in the air.

A hot-air balloon drifting toward Earth.

A long jumper in action.

A hot-air balloon drifting toward Earth is not an example of projectile motion because it does not have an initial horizontal velocity. In projectile motion, an object is launched with an initial velocity and then follows a curved path due to the influence of gravity. The volleyball, baseball, and long jumper all have an initial horizontal velocity and are subject to gravity, causing them to follow a curved trajectory. However, a hot-air balloon does not have an initial horizontal velocity and is carried by wind currents, resulting in a more vertical descent rather than a curved path.

Explanation

A hot-air balloon drifting toward Earth is not an example of projectile motion because it does not have an initial horizontal velocity. In projectile motion, an object is launched with an initial velocity and then follows a curved path due to the influence of gravity. The volleyball, baseball, and long jumper all have an initial horizontal velocity and are subject to gravity, causing them to follow a curved trajectory. However, a hot-air balloon does not have an initial horizontal velocity and is carried by wind currents, resulting in a more vertical descent rather than a curved path.

9. What type of quantity is the distance traveled by a car traveling 100 kilometers to the north?

Scalar

Vector

Neither

Both

The distance traveled by the car, 100 kilometers to the north, is classified as a vector quantity. Vector quantities have both magnitude (amount) and direction. In this case:

Magnitude: 100 kilometers (the distance traveled)
Direction: North

Therefore, because the travel distance includes a specific direction (north), it falls under the category of vector quantities. Scalars, in contrast, have magnitude only (e.g., speed, time). Hence, the correct answer is Vector.

Explanation

The distance traveled by the car, 100 kilometers to the north, is classified as a vector quantity. Vector quantities have both magnitude (amount) and direction. In this case:

Magnitude: 100 kilometers (the distance traveled)
Direction: North

Therefore, because the travel distance includes a specific direction (north), it falls under the category of vector quantities. Scalars, in contrast, have magnitude only (e.g., speed, time). Hence, the correct answer is Vector.

10. Which of the following is an example of projectile motion?

A helicopter taking off

A thrown baseball

A space shuttle being launched

A jet lifting off a runway

A thrown baseball is an example of projectile motion because it follows a curved path in the air due to the combined effects of its initial velocity and the force of gravity acting on it. As soon as the baseball leaves the pitcher's hand, it becomes subject to the force of gravity, causing it to follow a parabolic trajectory until it eventually lands on the ground. This type of motion, where an object is launched into the air and moves under the influence of gravity alone, is known as projectile motion.

Explanation

A thrown baseball is an example of projectile motion because it follows a curved path in the air due to the combined effects of its initial velocity and the force of gravity acting on it. As soon as the baseball leaves the pitcher's hand, it becomes subject to the force of gravity, causing it to follow a parabolic trajectory until it eventually lands on the ground. This type of motion, where an object is launched into the air and moves under the influence of gravity alone, is known as projectile motion.

11. Which of the following is the motion of objects moving in two dimensions under the influence of gravity?

Vertical velocity

Horizontal velocity

Dot product

Projectile motion

Projectile motion refers to the motion of objects that are launched into the air and move in two dimensions under the influence of gravity. It involves both vertical and horizontal velocities, as the object follows a curved path known as a projectile trajectory. The directrix is not relevant to this concept. Therefore, the correct answer is projectile motion.

Explanation

Projectile motion refers to the motion of objects that are launched into the air and move in two dimensions under the influence of gravity. It involves both vertical and horizontal velocities, as the object follows a curved path known as a projectile trajectory. The directrix is not relevant to this concept. Therefore, the correct answer is projectile motion.

12. Identify the following quantities as scalar or vectors: the speed of a snail, the time it takes to run a mile, and the free-fall acceleration.

Vector, scalar, scalar

Scalar, scalar, vector

Vector, scalar, vector

Scalar, vector, vector

The speed of a snail is a scalar quantity because it only has magnitude and no direction. The time it takes to run a mile is also a scalar quantity as it only represents a duration and has no direction. On the other hand, free-fall acceleration is a vector quantity as it has both magnitude (9.8 m/s²) and direction (downwards towards the center of the Earth).

Explanation

The speed of a snail is a scalar quantity because it only has magnitude and no direction. The time it takes to run a mile is also a scalar quantity as it only represents a duration and has no direction. On the other hand, free-fall acceleration is a vector quantity as it has both magnitude (9.8 m/s²) and direction (downwards towards the center of the Earth).

13. Which of the following does not exhibit parabolic motion?

A baseball is thrown to home plate.

A frog is jumping from land into the water.

A flat piece of paper is released from a window.

A basketball is thrown into a hoop.

A flat piece of paper does not exhibit parabolic motion because it lacks the necessary force or propulsion to follow a curved trajectory. Unlike the other options, which involve objects being thrown or propelled with force, the paper simply falls due to gravity without any initial velocity or additional force acting upon it. As a result, its motion is purely vertical and does not follow a parabolic path.

Explanation

A flat piece of paper does not exhibit parabolic motion because it lacks the necessary force or propulsion to follow a curved trajectory. Unlike the other options, which involve objects being thrown or propelled with force, the paper simply falls due to gravity without any initial velocity or additional force acting upon it. As a result, its motion is purely vertical and does not follow a parabolic path.

14. Which of the following is always positive?

Vector

Magnitude

Direction

Magnitude refers to the size or quantity of a vector or scalar quantity. It is always positive or zero. Scalars are quantities that are fully described by their magnitude (e.g., speed), while vectors have both magnitude and direction (e.g., velocity). The term "direction" doesn't inherently have a numerical value, and it's the orientation of a vector rather than a quantity with a positive or negative value.

Explanation

Magnitude refers to the size or quantity of a vector or scalar quantity. It is always positive or zero. Scalars are quantities that are fully described by their magnitude (e.g., speed), while vectors have both magnitude and direction (e.g., velocity). The term "direction" doesn't inherently have a numerical value, and it's the orientation of a vector rather than a quantity with a positive or negative value.

15. Which of the following is a coordinate system for specifying the precise location of objects in space?

Diagram

X-axis

Frame of reference

Y-axis

A coordinate system is a method used to define the position of objects in space. In this context, a frame of reference serves as a coordinate system that allows for the precise location of objects to be specified. It provides a set of axes, such as the x-axis and y-axis, which can be used to measure distances and determine positions accurately. By using a frame of reference, objects can be located and described based on their position relative to a fixed point or set of points, enabling precise spatial calculations and measurements.

Explanation

A coordinate system is a method used to define the position of objects in space. In this context, a frame of reference serves as a coordinate system that allows for the precise location of objects to be specified. It provides a set of axes, such as the x-axis and y-axis, which can be used to measure distances and determine positions accurately. By using a frame of reference, objects can be located and described based on their position relative to a fixed point or set of points, enabling precise spatial calculations and measurements.

16. What is the resultant velocity of a duck flying 10.0 m/s due south against a gust of wind with a speed of 2.5 m/s?

-7.5 m/s south

12.5 m/s south

7.5 m/s south

-12.5 m/s south

The duck is flying south at a speed of 10.0 m/s, but it is flying against a gust of wind with a speed of 2.5 m/s. To find the resultant velocity, subtract the wind's speed from the duck's speed:

$Resultant velocity = 10.0 m/s - 2.5 m/s = 7.5 m/s south$

Therefore, the resultant velocity of the duck is 7.5 m/s south. This calculation accounts for the wind's resistance, reducing the duck's effective speed.

Explanation

The duck is flying south at a speed of 10.0 m/s, but it is flying against a gust of wind with a speed of 2.5 m/s. To find the resultant velocity, subtract the wind's speed from the duck's speed:

$Resultant velocity = 10.0 m/s - 2.5 m/s = 7.5 m/s south$

Therefore, the resultant velocity of the duck is 7.5 m/s south. This calculation accounts for the wind's resistance, reducing the duck's effective speed.

17. Which of the following is a scalar quantity?

Velocity

Displacement

Force

Speed

Scalar quantities are defined solely by their magnitude (a numerical value) and lack any direction. Speed, which describes how fast an object is moving, fits this definition perfectly. In contrast, velocity, displacement, and force are vector quantities. Velocity incorporates both speed and direction (e.g., 60 mph north). Displacement refers to the overall change in position, including direction (e.g., 10 meters east). Force also has direction, indicating the push or pull exerted on an object (e.g., 5 Newtons downward).

Explanation

Scalar quantities are defined solely by their magnitude (a numerical value) and lack any direction. Speed, which describes how fast an object is moving, fits this definition perfectly. In contrast, velocity, displacement, and force are vector quantities. Velocity incorporates both speed and direction (e.g., 60 mph north). Displacement refers to the overall change in position, including direction (e.g., 10 meters east). Force also has direction, indicating the push or pull exerted on an object (e.g., 5 Newtons downward).

18. Which of the following exhibits parabolic motion?

A space shuttle orbiting Earth

A leaf falling from a tree

A stone is thrown into a lake

A train moving along a flat track

A stone thrown into a lake exhibits parabolic motion because it follows a curved path due to the combination of its initial horizontal velocity and the downward force of gravity. As the stone moves forward, gravity pulls it downward, causing it to curve downward in a parabolic trajectory. This motion is characteristic of objects that are launched with an initial velocity and experience a constant force acting vertically downward, resulting in a parabolic path.

Explanation

A stone thrown into a lake exhibits parabolic motion because it follows a curved path due to the combination of its initial horizontal velocity and the downward force of gravity. As the stone moves forward, gravity pulls it downward, causing it to curve downward in a parabolic trajectory. This motion is characteristic of objects that are launched with an initial velocity and experience a constant force acting vertically downward, resulting in a parabolic path.

19. What is the path of a projectile (in the absence of air resistance)?

A wavy line

Projectiles do not follow a predictable path.

A hyperbola

A parabola

In the absence of air resistance, a projectile follows a parabolic path. This is due to the influence of gravity acting downward while the projectile moves forward. The horizontal motion is uniform, meaning the horizontal velocity remains constant, while the vertical motion is uniformly accelerated, meaning the vertical velocity changes at a constant rate due to gravity. The combination of these motions results in a curved, parabolic trajectory, described mathematically by a quadratic equation. This predictable path is a key concept in physics, particularly in the study of projectile motion.

Explanation

In the absence of air resistance, a projectile follows a parabolic path. This is due to the influence of gravity acting downward while the projectile moves forward. The horizontal motion is uniform, meaning the horizontal velocity remains constant, while the vertical motion is uniformly accelerated, meaning the vertical velocity changes at a constant rate due to gravity. The combination of these motions results in a curved, parabolic trajectory, described mathematically by a quadratic equation. This predictable path is a key concept in physics, particularly in the study of projectile motion.

20. What results from multiplying or dividing vectors by scalars?

Vectors if multiplied or scalars if divided

Scalars if multiplied scalars

Scalars

Vectors

When you multiply or divide a vector by a scalar, the result is a vector. The direction of the vector remains the same, but its magnitude is scaled by the scalar. Multiplying by a scalar stretches or shrinks the vector, while dividing by a scalar has a similar effect but inversely. Scalars do not change the fundamental nature of the vector, which remains a vector.

Explanation

When you multiply or divide a vector by a scalar, the result is a vector. The direction of the vector remains the same, but its magnitude is scaled by the scalar. Multiplying by a scalar stretches or shrinks the vector, while dividing by a scalar has a similar effect but inversely. Scalars do not change the fundamental nature of the vector, which remains a vector.

21. Which trigonometric function, when multiplied by a vector's magnitude, gives the y-component of a vector oriented at an angle with respect to the x-axis in a coordinate system?

Cos θ

Cot θ

Sin θ

Tan θ

In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its y-component can be found using the sine function. The y-component (V_y) is equal to the vector's magnitude (V) multiplied by the sine of the angle (θ):

V_y=V sinθ

This relationship comes from the definition of the sine function in a right triangle, where the opposite side (y-component) is equal to the hypotenuse (vector's magnitude) multiplied by the sine of the angle. This is a fundamental concept in vector decomposition.

Explanation

In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its y-component can be found using the sine function. The y-component (V_y) is equal to the vector's magnitude (V) multiplied by the sine of the angle (θ):

V_y=V sinθ

This relationship comes from the definition of the sine function in a right triangle, where the opposite side (y-component) is equal to the hypotenuse (vector's magnitude) multiplied by the sine of the angle. This is a fundamental concept in vector decomposition.

22. A passenger on a bus moving east sees a man standing on a curb. From the passenger's perspective, the man appears to

Move west at a speed that is equal to the bus's speed.

Move west at a speed that is less than the bus's speed

Standstill

Move east at a speed that is equal to the bus's speed.

The passenger on the bus sees the man on the curb appear to move west at a speed that is equal to the bus's speed. This is because the bus is moving east, so the relative motion between the bus and the man is that the man appears to be moving in the opposite direction at the same speed as the bus.

Explanation

The passenger on the bus sees the man on the curb appear to move west at a speed that is equal to the bus's speed. This is because the bus is moving east, so the relative motion between the bus and the man is that the man appears to be moving in the opposite direction at the same speed as the bus.

23. From the teacher's perspective, how does a piece of chalk appear to fall when dropped while walking at a speed of 1.5 m/s?

Straight down

Straight backward

Straight down and forward

Straight down and backward

From the teacher's perspective, the chalk appears to fall straight down. This is because both the teacher and the chalk are moving forward at the same speed (1.5 m/s). When the chalk is released, it retains this horizontal motion. Since there is no relative horizontal movement between the teacher and the chalk, the only visible motion from the teacher's point of view is the vertical drop due to gravity. To an observer on the ground, the chalk would follow a parabolic path, but to the teacher, it seems to fall straight down.

Explanation

From the teacher's perspective, the chalk appears to fall straight down. This is because both the teacher and the chalk are moving forward at the same speed (1.5 m/s). When the chalk is released, it retains this horizontal motion. Since there is no relative horizontal movement between the teacher and the chalk, the only visible motion from the teacher's point of view is the vertical drop due to gravity. To an observer on the ground, the chalk would follow a parabolic path, but to the teacher, it seems to fall straight down.