Question

Neglect the effect of rotation of the earth. Suppose the earth suddenly stops attracting objects placed near its surface. A person standing on the surface of the earth will –
A) Fly up
B) Slip along the surface
C) Fly along a tangent to the earth’s surface.
D) Remain standing.

Answer 1

Hint: We should understand the reason for the attraction we experience on the surface of the earth. The earth is huge mass compared to any object in its surface and so the gravitational force has a great effect on it. This idea can be used to solve this problem.

Complete answer:
We know that the earth’s gravitational force keeps us on the planet without flying away. If that is the case, then what is force that is trying to pull us from the surface. We know that the earth is rotating on its axis. We also know that any rotational motion can produce a centrifugal force along the tangent at the point on the circle.
                                

So, the centrifugal force will pull us away which is opposed by the gravitational force.
i.e.,
\[\begin{align}
  & {{F}_{g}}={{F}_{c}} \\
 & \therefore mg=\dfrac{m{{v}^{2}}}{r} \\
\end{align}\]
Let us consider the situation given to us. It is said that there is no effect of rotation of earth on the person on the earth’s surface. That means there is no centrifugal force acting on the person.
i.e.,
\[{{F}_{c}}=0\]
Now, we are told that the attraction is also cancelled, this means the gravitational force also becomes zero. As a result, we can see that there is no force acting in the person. So, the person will be standing still.
This is the required solution.

The correct answer is option D.

Note:
The centrifugal force is an apparent force acting on a body which undergoes circular motion. It is the outward force which tempts the object to be thrown off from the circular path in a straight line along the tangent at that point due to the inertial effects.