Answer
Verified
367.2k+ views
Hint: Gravity is the force which pulls the objects down towards the ground and acceleration produced by this force is called the acceleration due to gravity.Gravitational acceleration is a quantity of vector, that is it has both magnitude and direction.
Complete step by step answer:
Acceleration due to gravity at the surface of earth is approximately \[9.8\,m/{{s}^{2}}\]. It is not the same everywhere. It keeps on decreasing as we go above the surface of earth.
As we go below the surface of earth, the variation in g(acceleration due to gravity) is given by:
\[g'=g\left( 1-\dfrac{h}{{{R}_{e}}} \right)\]
where,
\[g'=\] Actual acceleration due to gravity at a depth ‘h’ from the surface of earth
\[g=\] Acceleration due to gravity at the surface of earth \[=9.8m/{{s}^{2}}\]
\[h=\] Distance from the surface of the earth
\[\operatorname{R_e}=\] Radius of the earth
Now, at the centre of earth, \[h=\operatorname{Re}\]
\[g'=g\left( 1-\dfrac{{{R}_{e}}}{{{R}_{e}}} \right)\]
\[\therefore g'=0\]
Therefore, acceleration due to gravity at the centre of the earth is \[0\] and it keeps on increasing till we reach at the surface of the earth and after that it keeps on decreasing.
Note: Logically, we can understand this by, when we move inside the earth, the mass that exerts gravitational force on us decreases and hence at the centre of the earth the acceleration due to gravity becomes zero. Variation of g as we go above the surface of the earth is given by \[g'=\dfrac{g}{{{\left( 1+\dfrac{h}{{{R}_{e}}} \right)}^{2}}}\].
Complete step by step answer:
Acceleration due to gravity at the surface of earth is approximately \[9.8\,m/{{s}^{2}}\]. It is not the same everywhere. It keeps on decreasing as we go above the surface of earth.
As we go below the surface of earth, the variation in g(acceleration due to gravity) is given by:
\[g'=g\left( 1-\dfrac{h}{{{R}_{e}}} \right)\]
where,
\[g'=\] Actual acceleration due to gravity at a depth ‘h’ from the surface of earth
\[g=\] Acceleration due to gravity at the surface of earth \[=9.8m/{{s}^{2}}\]
\[h=\] Distance from the surface of the earth
\[\operatorname{R_e}=\] Radius of the earth
Now, at the centre of earth, \[h=\operatorname{Re}\]
\[g'=g\left( 1-\dfrac{{{R}_{e}}}{{{R}_{e}}} \right)\]
\[\therefore g'=0\]
Therefore, acceleration due to gravity at the centre of the earth is \[0\] and it keeps on increasing till we reach at the surface of the earth and after that it keeps on decreasing.
Note: Logically, we can understand this by, when we move inside the earth, the mass that exerts gravitational force on us decreases and hence at the centre of the earth the acceleration due to gravity becomes zero. Variation of g as we go above the surface of the earth is given by \[g'=\dfrac{g}{{{\left( 1+\dfrac{h}{{{R}_{e}}} \right)}^{2}}}\].
Recently Updated Pages
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Advantages and disadvantages of science
10 examples of friction in our daily life
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
10 examples of evaporation in daily life with explanations
One cusec is equal to how many liters class 8 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
How do you graph the function fx 4x class 9 maths CBSE