Question

Which of the following is a vector?
$(a){\text{ force}} \\\ {\text{(b) mass}} \\\ {\text{(c) energy}} \\\ {\text{(d) power}} \\\$

Answer 1

Hint – In this question think of the quantity from the given options that has both direction as well as magnitude. A vector quantity is that which has both of these mentioned hence the use of basic definition of vector will help to get the right answer.

Complete step-by-step solution -
As we know there are two types of quantity in a physical world:
$\left( 1 \right)$ Scalar quantity
$\left( 2 \right)$ Vector quantity.
Now scalar quantities are those which have only magnitude but not specific direction.
For example: Mass, energy, power, etc.
And vector quantities are those which have magnitude as well as specific direction.
For example: Force, acceleration, etc.
All bodies have a particular mass which does not depend upon the direction, on the other hand weight of the body is always directed downwards due to gravitational force of the earth's mass is a scalar quantity and weight is a vector quantity.
As we know according to Newton’s second law of motion force (F) is the product of mass (M) and acceleration (a).
$\Rightarrow F = Ma$
As we know that acceleration working on the body is always directed towards a particular direction so force working on the body is always directed in the same direction of the acceleration, therefore force and acceleration are vector quantities.
So force is a vector quantity.
Hence option (A) is the correct answer.

Note – In the first option we have force, we can recall many problems in which there are statements like a force of 20 kilo newton is directed towards a block, and this shows that the magnitude of the force is aligned to a specific direction proving it a vector. Mass need not be confused as a vector, in some problems there is a force mg that acts downwards, mg is the force and thus a vector however mass has no direction, the same applies to energy and power.