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The motion in a plane is the motion in two dimensions for example circular motion, projectile motion, etc. For this purpose, the two axes that we will be taking into consideration are the X-axis and the Y-axis. A motion of a boat in a river or the motion of throwing a rock are examples of motion in a plane. Quantities in physics can be classified as either scalars or vectors. The difference between the both is that unlike scalar, direction is associated with vector.
Scalar quantities are physical quantities that are totally defined by their magnitude or size only. Length, mass, density, speed, work, and so on are some examples.
Vector quantities are physical quantities that have a magnitude and a direction, both. They don’t abide by the ordinary laws of Algebra. They change if either the magnitude or direction or both the quantities change. These are represented by bold-faced letters or letters having an arrow over them. Velocity, displacement, acceleration, force, momentum, torque, and so on are some examples. A unit vector is used to specify the direction of any vector quantity.
Scalar and Vector Quantity
Multiple Choice Questions
Ques. Which of the following affects the angular velocity with its rate of change?
- Angular acceleration
- Angular Distance.
- Angular Displacement.
- torque
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Ans. (c) Angular Displacement.
Explanation: Angular velocity is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes. Thus the rate of change of angular velocity depends on angular displacement.
Ques. An object makes a displacement of 4 m due East from a point P and then makes displacement of 3 m due North. Its resultant displacement from P.
- 7 m
- 1 m
- 5 m
- 1.2 m
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Ans. (c) 5 m
Explanation: Let the point 4m from east of P be A. So PA is 4m and the point in the north be B such that AB is 3m. Therefore PBA is a right-angled triangle. The resultant displacement is equal to PB
PA2 + AB2 = PB2
42 + 32 = PB2
16 + 9 = 25 = PB2
PB = 5m
Ques. What is the name given to a path followed by a projectile?
- Territory
- Treasury
- Tractor
- Trajectory
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Ans. (d) Trajectory
Explanation: The path that an object with mass in motion follows through space as a function of time is called a trajectory or flight path. The total distance between the source and the target position is called the slant range. The angle formed between them is called the Inclination Angle.
Ques. Zero vector is also called as?
- Point vector
- Unit Vector
- Null vector
- None of the above
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Ans. (c) Null vector
Explanation: The vector with zero magnitudes is called a zero vector or null vector. The direction of the null vector is not specified.
Ques. Vectors are quantities that are having
- Magnitude
- Direction
- Both a and b
- None of the above
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Ans. (c) Both a and b
Explanation: Scalar quantities like mass, density have a definite magnitude. Vector Quantities are physical quantities that have both a magnitude and a direction. The vector quantities change values with changes in magnitude and direction.
Also Read: Angular Motion
Ques. On multiplying a vector with a scalar, the magnitude changes. What happens to its direction?
- remains the same
- Changes direction
- Both a and b
- None of the above
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Ans. (a) remains the same
Explanation: The product of a vector and scalar quantity has an increase in magnitude as both scalar and vector quantity have magnitude, whereas the direction of the product takes the direction of the vector only in the product. Hence it remains the same.
Ques. The unit vectors i, j, k are along the x, y, and z axes respectively are?
- Parallel to each other
- Perpendicular to each other
- Both a and b
- None of the above
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Ans. (b) Perpendicular to each other
Explanation: The angle between each axes x,y, and z is 90°. As the axes are perpendicular to each other, the unit vectors i, j and k are also perpendicular to each other.
Also Read: Unit of Momentum
Ques. An object that is in flight after being thrown or projected from its source position is called?
- Vector
- Magnitude
- Projectile
- Trajectory
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Ans. (c) Projectile
Explanation: Vector and scalar are quantities with certain characteristics. A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. The object involved in the flight is called a projectile.
Ques. The direction of velocity at any given point on the path of the object is
- perpendicular to the path
- parallel to the path
- tangential to the path
- None of the above
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Ans. (c) tangential to the path
Explanation: The direction of velocity at any given point on the trajectory or path of an object is tangential to the path at that point and is along the direction of motion.
Ques. The unit vector associated with vector A is given by
- A / A
- A / |A|
- |A| / A
- None
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Ans. (b) A/|A|
Explanation: The Unit Vector is denoted by the representing letter with the symbol ‘^’, which is called a cap or hat, such as \(\hat{a}\). It is given by \(\hat{a}\) = a / |a| where |a| is for the magnitude of the vector of a.
Ques. What is the relation between the magnitude of the displacement and the path length between two points?
- Less than the actual path
- Equal to the path
- Greater than the actual path length
- Both a and b
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Ans. (d) Both a and b
Explanation: Displacement is the least or shortest straight-line path between two points. The magnitude of displacement is equal to the path length if the chosen path is of the shortest length. But if the travel path is longer than that, then the displacement magnitude will be less than the actual path.
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