Question

Which of the following statements is/are false?
A. Mass, speed and energy are scalar quantities.
B. Momentum, force and torque are vector quantities.
C. Distance is a scalar quantity but displacement is a vector quantity.
D. A vector has only magnitude whereas a scalar has both magnitude and direction.

Answer 1

Hint: A quantity not dependent on direction is considered a scalar quantity. There are two characteristics of the vector quantities, a magnitude and direction. Scalar amounts that have magnitude.

Complete step by step answer:
Mass: The substance of matter in a body is mass. Everywhere in the world it is the same. Regardless of the manner in which you travel, the quantity of matter within you will never change. That's why the quantity is scalar.
Speed: Speed needs only a numerical value for its representation (e.g.\[13{\text{ km/hr}}\]) and not a direction, and this is why speed is not a vector but a scalar quantity.
Energy: We may assume the energy expended is equal to the amount of work performed.
\[{\text{Energy}} = {\text{Work}} = F \times s\], here vector quantity is both the power and the time. And we know the scalar quantity is given by the product of two vector quantities. Then we can assume the quantity of energy is scalar.

Momentum: Momentum is of both magnitude and direction. Hence, momentum is a quantity of the vector.
Force: Force is a vector quantity and it has both magnitude and direction. Even so you may have a negative force; the negative simply means that it is moving in the other direction.
Torque: Torque is just the cross product of the vector of the radius (from the centre of symmetry to the point of force application) and the vector of force. Hence, torque is a vector quantity.

Distance means the separation between points and is the range you calculate when comparison with the units of length. Whereas, displacement refers to a shift in position which not only means length but also direction.

Hence, option D is false.

Note:Whenever a scalar quantity is involved, it has only magnitude, whereas a vector has both magnitude and direction. In addition to this, vector quantities also follow the parallelogram law of vector addition.