Question

differentiate between acceleration due to gravity and universal gravitational constant ​

Answer 1

Answer:

Difference between Universal gravitational constant and acceleration due to gravity

Universal gravitational constant is represented by G.

acceleration due to gravity is represented by g.

Universal gravitational constant value is 6.673× 10^-11 Nm² kg^-2

acceleration due to gravity value on earth is 9.8 m/s²

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Answer 2

Explanation:

G[Universal gravitational constant]:

Let m1 =m2=1 and r=1.

We know that , F=G×m1×m2/r²

F=G×1×1/1²

F=G

Thus Universal gravitational constant is equal to the force of attraction acting between the two bodies each of unit mass, whose centers are placed unit distance apart.

Gravitational constant is a scalar quantity. It's value is same throughout the universe and is independent of the nature and size of the bodies as well as the nature of the medium between the bodies. The value of G in SI unit is

$6.67 \times {10}^{11} N {m}^{2}kg {}^{ - 2}$

and in CGS system it's value is

$6.67 \times {10}^{ - 8} dyne \: cm {}^{2} {g}^{ - 2}.$

The dimensional formula for G is

$\frac{f {r}^{2} }{m1m2} = \frac{(ML {T}^{ - 2}) }{m \times m} = ( {M}^{ - 1} {L}^{3} {T}^{ - 2} )$

Note:

Newton's law of gravitation holds good for objects lying at very large distances and also at very short distances. It fails when the distance between the objects is less than 10^-9 m(i.e.,of the order of intermolecular distances)

Acceleration due to gravity [g]:

The acceleration which is gained by any object due to the gravity is known as acceleration due to gravity. It is a vector quantity. It's SI unit is m/s² and it's CGS unit is cm/s². The general value of 'g' is 9.8 m/s² or 980 cm/ s². It's formula is

$\frac{Gm}{ {r}^{2} } .$

It's dimensional formula is

$g = a = \frac{velocity}{time} \\ \frac{ \frac{displacement}{time \: } }{time} = \frac{ \frac{L}{T} }{T } \\ = ({M}^{0} {L}^{1} {T}^{ - 2})$