Which one of the following statements is correct?
(a) Energy and work are scalars
(b) Force and work are vectors
(c) Energy, momentum and velocity are vectors
(d) Force, momentum and velocity are scalars
(a) is correct.
Force, momentum and velocity are vectors. Energy and work are scalar quantities.
The correct statement is:
(c) Energy, momentum, and velocity are vectors.
To determine which statement is correct, we need to understand the definitions and characteristics of scalars and vectors.
Scalars are physical quantities that have only magnitude, or size. Examples of scalars include temperature, mass, time, and energy. Scalars are represented by a single value or number.
Vectors, on the other hand, are physical quantities that have both magnitude and direction. Examples of vectors include displacement, velocity, acceleration, force, and momentum. Vectors are typically represented by arrows, where the length of the arrow represents the magnitude, and the direction of the arrow represents the direction.
Now, let's analyze the statements:
(a) Energy and work are scalars: This statement is incorrect. Energy and work are both examples of scalar quantities. Energy is a scalar because it only has magnitude, such as the energy of an object is measured in joules (J). Similarly, work is also a scalar quantity, and its units are also joules (J). So, it can be said that statement (a) is correct.
(b) Force and work are vectors: This statement is partially correct. Work is scalar, not a vector. However, force is indeed a vector quantity because it has both magnitude and direction. Force is measured in units such as Newtons (N). So, statement (b) is incorrect.
(c) Energy, momentum, and velocity are vectors: This statement is incorrect. Among these three quantities, energy is a scalar as discussed earlier. However, both momentum and velocity are vector quantities. Momentum is the product of an object's mass and velocity and has both magnitude and direction. Similarly, velocity is a vector quantity representing the speed and direction of an object's motion. Therefore, statement (c) is incorrect.
(d) Force, momentum, and velocity are scalars: This statement is incorrect. Force, momentum, and velocity are all vector quantities, not scalars. As mentioned earlier, force and velocity have both magnitude and direction, while momentum is the product of mass and velocity and also has both magnitude and direction. So, statement (d) is incorrect.
To summarize, the correct statement is (a) Energy and work are scalars.