Question

Due to a force of $(6\widehat i + 2\widehat j)N$ the displacement of a body is $(3\widehat i - \widehat j)m,$ then the work done is?
$A.{\text{ 16j}} \\\ {\text{B}}{\text{. 12j}} \\\ {\text{C}}{\text{. 8j}} \\\ {\text{D}}{\text{. zero}} \\\$

Answer 1

In Physics, the work done is the force causing displacement of the object. It is the scalar product although the force and displacement are the vector quantities. Vector quantities are the quantities whose direction and magnitude both are important. Use formula for work done, $W = F.d$ where F is the force and d is the displacement. And work done is measured in joules.

Complete step by step answer:
Force, $F = (6\widehat i + 2\widehat j)N$
Displacement, $d = (3\widehat i - \widehat j)m$
Now, by the formula-
Work done is $W = F.d$
Place the given values in the above equation –
$W = (6i + 2j) \times (3i - j)$
Multiply the corresponding product with “i” and “j” terms-
$W = (6 \times 3) + (2 \times - 1) \\\ \implies W = 18 - 2 \\\$
(As the product of one positive and one negative terms gives negative term)
$\therefore W = 16 J$

Hence, from the given multiple choices – the option A is the correct answer.

Additional Information:
The unit of work (w) in the international systems of units is named in the honor of the English physicist James Prescott Joule as the joules. One joule can be defined as the amount of work done by the force of one Newton which displaces the body through the distance of one metre in the direction of the force applied.

Note:
Dot product in physics is the product of two vectors. It is the sum of the products of the corresponding values in the vectors That is i, j and k. Remember the dot products as $i.i = j.j = k.k = 1$. Work done can be expressed in various ways and the MKS unit of work done is Newton into meter, but we used its SI unit, i.e. Joule as per the required solution.