Derive a relation between the Universal Gravitational Constant ([tex]G[/tex]) and acceleration due to gravity ([tex]g[/tex]).

suppose earth is a soid sphere which will attract the body towards its centre.So, acc. to law of gravitation force on the body will be, F=G m1m2/R^2 but we now that F=ma and here accleration(a)=accleration due to gravity(g),so force applied by earth on will also be mg replace above F in formula by mg and solve, F=G mE m/R^2 ( here mE is mass of earth and m is mass of body) mg=G mEm/R^2 so, g =G*mE/R^2

Answered by vbv | 2024-06-10

suppose earth is a soid sphere which will attract the body towards its centre.So, acc. to law of gravitation force on the body will be, F=G m1m2/R^2 but we now that F=ma and here accleration(a)=accleration due to gravity(g),so force applied by earth on will also be mg replace above F in formula by mg and solve, F=G mE m/R^2 ( here mE is mass of earth and m is mass of body) mg=G mEm/R^2 so, g =G*mE/R^2

Answered by jatin | 2024-06-10

The relationship between the Universal Gravitational Constant G and acceleration due to gravity g is given by the formula g = R E 2 ​ G M E ​ ​ , where M E ​ is the mass of the Earth and R E ​ is the radius of the Earth. This equation shows how G plays a critical role in determining the force of gravity experienced at the Earth's surface. Using values for M E ​ and R E ​ yields an average g of about 9.81 m/s 2 .
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Answered by vbv | 2024-12-23