Chapter 7, Problem 7.1QQ

To determine

The work done by the gravitational force during a short interval in which the Earth moves through a displacement in its orbital path.

Answer to Problem 7.1QQ

Option (a) zero.

Explanation of Solution

The Earth revolve around the sun in an orbit and the orbit is perfectly circular.

Formula to calculate the work done by the gravitational force is,

    $W_{\text{g}}=F\Delta r$

Here, $F$ is the gravitational force exerted by the sun on the earth, $W_{\text{g}}$ is the work done by the gravitational force and $\Delta r$ is the displacement of the earth around the sun in an orbit.

Since, the Earth moves through a displacement in its orbital path and the orbital path is perfectly circular. So, the total displacement of the Earth in its orbital path is zero.

Substitute $0$ for $\Delta r$ to find $W_{\text{g}}$.

  $\begin{array}{c}{W}_{\text{g}}=F\times 0\\ =0\end{array}$

Thus, the work done by the gravitational force during a short interval in which the Earth moves through a displacement in its orbital path is zero.

Conclusion:

The work done by the gravitational force is zero and the option (a) is zero. Thus option (a) is correct.

The work done by the gravitational force is zero but the option (b) is positive. Thus option (b) is incorrect.

The work done by the gravitational force is zero but the option (c) is negative. Thus, option (c) is incorrect.

The work done by the gravitational force is zero. It means the work done can be determined. Thus, option (d) is incorrect.