Answer
414.3k+ views
Hint: First, calculate the gravitational force that the solid sphere exerts on the given point mass by using the formula for gravitational force. Then use the concept of shell theory and calculate the force exerted by the shell.
Complete step by step answer:
Let us first calculate the force exerted on the mass m by the solid sphere. The gravitational force on a point mass m located at a distance of x (x > R) from the centre of a sphere of mass M is given as $F=\dfrac{GMm}{{{x}^{2}}}$.
This means that the force exerted by the given solid sphere on the point mass is equal to $\dfrac{GMm}{{{x}^{2}}}$.
Let us now understand about the gravitational force exerted by a spherical shell on a [point mass located inside it. Suppose a point mass is located inside a spherical shell. Now, let us consider the shell made up of small elements of equal masses. Then the point mass will experience gravitational forces due to all the small elements in all the directions such that the net force on the point mass is zero. This concept is according to the shell theory.
Therefore, when a point mass is placed inside a spherical shell, its experiences no force due to the shell.
Hence, in the given case the net force exerted on the point mass m by the shell is zero. This means that the net force experienced by the point mass is equal to $\dfrac{GMm}{{{x}^{2}}}$.
Hence, the correct option is A.
Note: The direction of the gravitational force that a solid sphere exerts on a point mass situated outside the sphere is always towards the centre of mass of the sphere. If the mass of the sphere is uniformly distributed then the centre of mass will be at its geometrical centre.
Complete step by step answer:
Let us first calculate the force exerted on the mass m by the solid sphere. The gravitational force on a point mass m located at a distance of x (x > R) from the centre of a sphere of mass M is given as $F=\dfrac{GMm}{{{x}^{2}}}$.
This means that the force exerted by the given solid sphere on the point mass is equal to $\dfrac{GMm}{{{x}^{2}}}$.
Let us now understand about the gravitational force exerted by a spherical shell on a [point mass located inside it. Suppose a point mass is located inside a spherical shell. Now, let us consider the shell made up of small elements of equal masses. Then the point mass will experience gravitational forces due to all the small elements in all the directions such that the net force on the point mass is zero. This concept is according to the shell theory.
Therefore, when a point mass is placed inside a spherical shell, its experiences no force due to the shell.
Hence, in the given case the net force exerted on the point mass m by the shell is zero. This means that the net force experienced by the point mass is equal to $\dfrac{GMm}{{{x}^{2}}}$.
Hence, the correct option is A.
Note: The direction of the gravitational force that a solid sphere exerts on a point mass situated outside the sphere is always towards the centre of mass of the sphere. If the mass of the sphere is uniformly distributed then the centre of mass will be at its geometrical centre.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)