Question

What is the area of Force (F)-Displacement (S) graph?
(a) Work Done
(b) Power
(c) Potential Energy
(d) Kinetic Energy

Answer 1

Hint: Area under the curve is basically the integration of the whole quantity. But we will solve this question by trial and error method, in which we will consider all the quantities and derive the relation between Force and displacement and based on that we will find the area under curves in each quantity and on the basis of that we will find the answer.

Complete step by step answer:
We will solve this problem by trial and error method so, for that we will consider each and every option so,
Considering option (a) that is, work done, Work done can be defined as displacement of a body due to constant force acting on it. It can be shown mathematically as, $W=F\centerdot s$. Now, as the force is constant the displacement also remains constant so the graph will be straight line. And the area under the curve for the graph will be Work done. It can be seen in graph as,

Considering option (b) that is power, Power is defined as work done by body per unit time. And work done is displacement of the body due to force acting on it. It can be shown mathematically as, $P=\dfrac{W}{t}=\dfrac{Fd}{t}$. Now here the force will not be constant rather than that it will change with respect to time, so, the graph will not be straight line and area under curve for graph of force-displacement will be power.
Considering option (c) that is potential energy, Potential energy of the system is stored in the system when the body applies force in the opposite direction of force acting on the body. It can be shown mathematically as, $P=F\centerdot d$. Here, the work done will be in the form of potential energy but the direction does not remain constant and the graph under the curve will be potential energy.
Considering option (d) that is Kinetic, Kinetic energy of the system is energy of system due to which the system performs motion, it can be shown as, $k=\dfrac{1}{2}m{{v}^{2}}=\dfrac{1}{2}m{{\left( \dfrac{d}{t} \right)}^{2}}$, here also the values of kinetic energy changes exponentially so the graph also changes and the area under curve will be kinetic energy.
So, considering all the options it can be said that the area under the curve for the graph of Force-Displacement is work done.
Hence, option (a) is the correct answer.

Note: Work done can be given as displacement of the body due to force acting on it. In different cases force in different ways such as, in case of thermal energy the work done by the gas is given by change in volume due to external heat supplied. In electrical energy, work done is given by the electric supply required to pass one electric charge from one end to another end. So, in different cases work done changes. So, here we have considered the most basic which is given in the question.