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Question: What is the range of gravitational force? A. \(10^{-2}\) m B. \(10^{-15}\) m C. Infinite D. ...

What is the range of gravitational force?
A. 10−210^{-2} m
B. 10−1510^{-15} m
C. Infinite
D. 10−1010^{-10} m

Explanation

Solution

Hint: Recall that the expression for gravitational force experienced by an object is given byGMmr2\dfrac{GMm}{{{r}^{2}}}.

Complete step by step solution:
Each mass in the universe exerts a force on another mass which attracts it towards its center. This is called the gravitational force. Though, mainstream gravitational force refers to celestial bodies attracting smaller objects, however the law of gravitation applies to each and every mass in the universe. Thus, even a human being attracts a tree and vice versa.
The expression for the gravitational force (Fg) exerted by a mass (M) on another mass (m), where the displacement between the centers of the two masses is (r) is given by
Fg→=GMmr2r^\overrightarrow{{{F}_{g}}}=\dfrac{GMm}{{{r}^{2}}}\widehat{r}
Thus, the direction of this force on mass m is towards the center of mass M as seen in the expression by the unit vectorr^\widehat{r}. Here G is the universal gravitational constant with value6.67×10−11m3kg−1s−26.67\times {{10}^{-11}}{{m}^{3}}k{{g}^{-1}}{{s}^{-2}}.
As seen from the expression, the magnitude of the gravitational force depends inversely on the square of the radial distance between the centers of the two masses. Thus, essentially, the force can only fall to zero, when the denominator that is r becomes infinite.
Therefore, in essence the range of gravitational force is infinite.
So, the correct option is C) infinite.

Note: Students might think since gravitational force falls off as the square of the distance from the mass, it may not have much range and may be tempted to mark the other answers. However, this is a wrong thinking process.
From the mathematical equation it can clearly be seen, even at very large distances, the gravitational force may become very minute and tend to zero, however it can be considered absolutely zero, when the denominator of the expression becomes infinite, that is the straight line distance from the center of the body is considered to be infinite.