Question

Obtain
a relation between acceleration due to gravity (g) and
gravitational constant (G)​

Answer 1

${ \huge \bf { \mid{ \overline{ \underline{Question}}} \mid}}$

Obtain a relation between acceleration due to gravity (g) and gravitational constant (G)?

$\huge{\bold{\underline{\underline{Answer}}}}$

$\huge{\bold{\underline{Given:-}}}$

• G = Universal Gravitational constant.
• g = Acceleration due to gravity.

$\huge{\bold{\underline{Explanation:-}}}$

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We know, From Universal law of Gravitation,

$\large{\boxed{\tt F = \dfrac{GMm}{R^2}}}$

• F = Gravitational Force
• M = Mass of the Planet.
• m = Mass of the Particle.
• R = Radius of the Planet.

But we Know, the Gravitational Force is supplied by the Weight of the body.

Substituting,

$\large{\tt \leadsto W = \dfrac{GMm}{R^2}}$

$\large{\leadsto}$ W = mg

$\large{\tt \leadsto mg = \dfrac{GMm}{R^2}}$

$\large{\tt \leadsto \cancel{m}g = \dfrac{GM\cancel{m}}{R^2}}$

$\huge{\boxed{\boxed{\tt g = \dfrac{GM}{R^2}}}}$

Hence derived!

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Inference:-

• Acceleration due to gravity (g) is Directly proportional to Universal Gravitational constant. I.e $\large{\tt g \propto G}$

• Acceleration due to gravity (g) is Directly proportional to Mass of Planet. I.e $\large{\tt g \propto M}$

• Acceleration due to gravity (g) is inversely proportional to Radius of Planet I.e $\large{\tt g \propto \dfrac{1}{R}}$

• Acceleration due to gravity is independent of Mass of the Particle.

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Answer 2

Gravitational Acceleration: g = (G × Mass)/(distance from the center)2. Comparing gravitational accelerations: acceleration at position A = acceleration at position B × (distance B/distance A)2.