Answer

Verified

35.1k+ views

**Hint:**Work is said to be done when a force produces motion in an object. The work done can be defined as the product of the force F and the displacement produced in the object, x. In a graphical form, F and x can be multiplied, and the area gives us the total value of the work done.

**Complete step by step answer:**

In a graphical representation of F vs x, we can integrate the curve and/or find the area enclosed between the two quantities.

This is the equivalent of multiplying in both quantities.

So, In the given graph we can divide the complex shape formed, into 2 simple shapes namely: A rectangle and a triangle.

Finding out areas of both these figures and adding them gives the value of total work done.

Area of triangle, ${A_1} = \dfrac{1}{2}bh$

From the graph, $b = 6 - 3 = 3$

$h = 3$

$\therefore {A_1} = \dfrac{1}{2} \times 3 \times 3$

${A_1} = 4.5Nm$

Now, Area of rectangle (square here)

${A_2} = {a^2}$

Where the side length, $a = 3$

${A_2} = {3^2}$

${A_2} = 9Nm$

The total work done, W is defined as:

$W = {A_1} + {A_2}$

$W = 4.5 + 9$

$W = 13.5Nm{\text{ or }}13.5J$

**The correct option is (A).**

**Additional Information**

Work done is highly dependent on the displacement of the body, no matter how much force is applied, if displacement or deformation of the body is zero, work done remains zero. It is a scalar quantity, but it is also a dot product of two vector quantities.

**Note:**If the shapes are given in forms of functions, then the work done can be calculated by integrating the function and applying limits, and adding up all the integrals. Even this question can be solved as an integral, but applying the formula for area simple shapes makes it easier to solve.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Other Pages

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Oxidation state of S in H2S2O8 is A 6 B 7 C +8 D 0 class 12 chemistry JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main

The strongest oxidising agent among the following is class 11 chemistry JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main