Question

Two point masses $m$ and $2m$ are placed at points $\text{A}$ and $\text{B}$ as shown in the figure. $E$ represents the magnitude of net gravitational field strength. As we move from $\text{A}$ to $\text{B}$

• A. $E$ will first increase then decrease.
• B. $E$ will first decrease then increase
• C. $E$ decreases throughout.
• D. $E$ remains constant.

Answer 1

The correct option is B $E$ will first decrease then increase

Gravitational field at distance $r$ due to point mass $m$,
$$E=\frac{Gm}{r^2}$$ Consider $E_m$ and $E_{2m}$ are the gravitational field intensities at any distance due to masses $m$ and $2m$ respectively.

At point $\text{A}$:
Electric field due to mass $m$
$E_m\to \infty [r\to 0]$


At point $\text{B}$:
Electric field due to mass $2m$,
$E_{2m}\to \infty [r\to 0]$

Consider a point $\text{P}$ where, the $E_m$ and $E_{2m}$ are equal but opposite in direction. So the net electric field, $E_{net}=0$

Thus, as we move from $\text{A}$ to $\text{B}$, field strength $E$ first decreases to zero at point $\text{P}$ then again increases till point $\text{B}$.

Hence, option (b) is the correct answer.

Why this question: This is an important question not only in gravitation, but also in electrostatics. This concept will develop the analytic skills of the student in judging the direction of gravitational field.