Question

Calculate the value of acceleration due to gravity g using the relation between g and G. plz solve it

Answer 1

$\boxed{F = m×g}$ ••••••••eq1

$\boxed{F = GMm/d²}$ ••••eq2

where ,

F = the force of gravity (Fgrav) with which an object of mass m was attracted to the earth

d = distance from the center of the object to the center of the earth.

M = mass of earth

G = universal gravitational constant

g = acceleration due to gravity

substitute both eq1 and eq2 ,we get

m*g = GMm/d²

$\boxed{g = GM/d²}$

g = [(6.673×10^-11N-m²)×(5.98×10²⁴kg)] /(6.38×10⁶m)²

g = 9.8 m/s²

hope it helps you...

Answer 2

Given,

Acceleration due to gravity, g

Gravitational Constant, G

To find,

The Value of Acceleration due to gravity

Solution,

Acceleration gained by an object due to force of gravity is known as acceleration due to gravity.

We know that,

Gravitational constant,  G=6.67×10^-11Nm²kg−².  

Mass of earth, Me = 6 × $10^{24}$ kg.

Mass of object = m

Radius of earth = Re= 6.4×$10^{6}$m

We know,

                 g = G × Me/R²

               g = 6.67 × 10^-11 × 6 × 10^24 /(6.4 × 10^6)² m/s²

               g = 6.67 × 6 × 10/ 6.4 × 6.4 m/s²

               g = 9.8 m/s²

Hence the value of acceleration due to gravity is 9.8 m/s².