Question

If you move from Delhi to Mumbai, what work is done by the earth? (Assume that both cities are at the same sea-level, \[d\] is the distance and \[m\] is your mass)
A) mgd
B) 0
C) -mgd
D) Can’t be obtained

Answer 1

Hint: If work is done on a body, the energy of the body changes. It may either increase or decrease depending upon how that work is done. The energy of a body is the sum of its kinetic energy (due to motion) and the potential energy (due to its position). Hence if we find the change in energy while moving from Delhi to Mumbai, we can find the work done.

Formula Used:
 \[W=\overrightarrow{F}.\overrightarrow{d}\]

Complete step by step solution:
The work done by a body when acted upon by a force \[\overrightarrow{F}\] that causes a displacement of \[\overrightarrow{d}\] is given as follows:
\[\begin{align}
  & W=\overrightarrow{F}.\overrightarrow{d} \\
 & \Rightarrow W=F\times d\times \cos \theta \\
\end{align}\]
Now since no explicit information is given about any force being acted on us, we’ll just consider the effect of earth’s gravity
The force applied by earth on us will thus be equal to our weight which can be given as \[F=mg\] where \[g\] is the acceleration due to gravity on the earth’s surface
The displacement in our position is along the earth’s surface and as such the angle between the force acting on us and our displacement will be \[{{90}^{\circ }}\] and we know very well that \[\cos {{90}^{\circ }}=0\]
Substituting these values in the expression of work we obtained in the beginning, we get
\[\begin{align}
  & W=mg\times d\times \cos {{90}^{\circ }} \\
 & \Rightarrow W=0(\because \cos {{90}^{\circ }}=0) \\
\end{align}\]

Hence, No work is done by the earth and the correct option is (B).

Note:We can also use the concept of change in energy to arrive at the same conclusion. Since there is no elevation in the height of the body above the earth’s surface, change in the potential energy will be zero and the change in the kinetic energy will be zero as well since there is no velocity change involved. Hence the net change in energy is zero and the work done is zero as well.