Question

A point mass \[{{m}_{0}}\] is placed at a distance \[\dfrac{R}{3}\] from the centre of a spherical shell of mass M and radius R. The gravitational force on the point mass \[{{m}_{0}}\] is
\[\begin{align}
  & \text{A}\text{. }\dfrac{9GM{{m}_{0}}}{{{R}^{2}}} \\
 & \text{B}\text{. }\dfrac{GM{{m}_{0}}}{{{R}^{2}}} \\
 & \text{C}\text{. Zero} \\
 & \text{D}\text{. }\dfrac{4GM{{m}_{0}}}{{{R}^{2}}} \\
\end{align}\]

Answer 1

Hint: The gravitational force is the force of attraction due to mass of an object. This force is an attractive force in between two objects with masses placed at some distance from each other. Here the distance is given and by using the gravitational force formula we can find the answer in terms of masses of objects and its distance.

Formula used:
\[{{F}_{G}}\text{=}\dfrac{GMm}{{{r}^{2}}}\]

Complete step-by-step answer:
Gravitational force is an attractive force which pulls two objects towards each other due to their masses which attracts each other towards its centre. Suppose two masses M and m are kept at a distance r from each other (as shown in figure), then the gravitational force is given by

\[{{F}_{G}}\text{=}\dfrac{GMm}{{{r}^{2}}}\]
Where G is the gravitational constant.
Now, according to question bodies of masses M and \[{{m}_{0}}\] are apart from each other by a distance \[\dfrac{R}{3}\] which can be shown diagrammatically as below.

Then the gravitational force will be given as
\[\begin{align}
  & {{F}_{G}}\text{=}\dfrac{GMm}{{{\left( \dfrac{R}{3} \right)}^{2}}} \\
 & {{F}_{G}}=\dfrac{9GMm}{{{R}^{2}}} \\
\end{align}\]

So, the correct answer is “Option A”.

Additional Information: Gravity is a special case of gravitational force where earth is one object and any other body on the surface of the earth is the second object. Hence gravity is the gravitational pull experienced by an object towards the earth.

Note: People often get confused in acceleration due to gravity and the gravitational constant. Acceleration due to gravity is an acceleration with which an object falling freely towards the earth will have. Whereas, gravitational constant is the gravitational force which is experienced by the unit masses kept at a distance away.