Question

Work done upon a body is
A. A vector quantity
B. A scalar quantity
C. Always positive
D. Always negative

Answer 1

Hint: Work can be defined as the product of the component of the force in the path of the displacement and the magnitude of this displacement. Hence we can find whether the work is a scalar or a vector quantity by defining the terms related to it. Also, mention the expression for the work done.

Complete step by step solution:
We can give the expression for work as,
\[W = \left( {Fcos\theta } \right)d = F.d\]
Where $W$ is the work done by the acting force, \[F\] is the force, $d$ is the displacement caused by the force and, $\theta $ is the angle between the force and the displacement vectors.
Work done by a force operating on a body is:
When the path of motion of the body and the force operating in the same direction, work done is positive.
When the direction of motion of the body and the force operating on the body is opposite, work done is negative.
When the force is operating at a right angle to the direction of motion of the body, work done is taken as zero.
As it has only magnitude and the direction isn’t accountable, so it is a scalar quantity. Hence option B is correct.

Note:
We can also relate the work done to the total force acting on the body and the total energy of the system. As work done is the same as the change in kinetic energy acting on the body, we can also get the work done by finding its total energy. Once an object slows down, its absolute kinetic energy is less than its primary kinetic energy, the difference in its kinetic energy is negative, and the net work done on it is also negative.