Question

The work done to project a body with a certain velocity is $W$. What extra work done is required to be done to double its velocity:
A. $W$
B. $2W$
C. $3W$
D. $4W$

Answer 1

In order to answer this question, first we will observe the given work done to project a body with a certain velocity and then identify which type of energy it is and then apply the formula of it in terms of the velocity of the body, to find the required extra work done.

Complete step by step answer:
In the given work, as we can observe that, work is done by virtue of motion, so:
Work is equals to the kinetic energy:-
$W = K.E = \dfrac{1}{2}m{v^2}$
where, $m$ is the mass of the given body which is projected and $v$ is the velocity at which work is done to project the body.
Now, according to the question:-
If the velocity would be doubled, then-
$W = 2 \times 2 = 4\,times$ extra work is done.
Therefore, $4W$ is the extra work required to be done to double its velocity.

Hence, the correct option is D.

Note: Work has been done on a moving object, it has kinetic energy. When work is completed, energy is transferred from one form to the kinetic energy of a moving item. To bring the thing back to rest, the same amount of effort would be required to stop it again.