Question

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

Answer 1

Answer:

The G is found in the universal gravitation law ( F = GmM/r^2) and Newton second law (w= mg) so that , if F=w, then, g = GM/r^2 , M mass of earth and r its radius, so using the values we get g=9.8 m/s^2.

Answer 2

Given:

• Gravitational constant (G) = 6.67×$10^{-11}$ N$m^2$ $Kg^{-2}$
• Mass of earth (M) = 6×$10^{24}$ Kg
• The radius of the earth (R) = 6.4×$10^6$ m

To Find:

• The value of acceleration due to gravity (g) by using gravitational constant and acceleration due to gravity relationship.

Solution:

Let the mass of the object be "m".

We know the relationship between G and g,

⇒ g = (G×M)/$R^2$ → {equation 1}

The above relation is derived from newton's second law and universal gravitation law.

On substituting the given values in equation 1 we get,

⇒ g = $\frac{6.67*10^{-11}*6*10^{24}}{(6.4*10^6)^2}$

In the above step, we multiply the terms in denominator and numerator and add their respective powers since the bases are the same.

⇒ g = 40.2×$10^{13}$ / 40.96×$10^{12}$  {divding the terms and adding the powers due to same bases}

⇒ g = 0.981×$10^{1}$ = 9.8 m/$s^2$

∴ The value of acceleration due to gravity = 9.8 m/$s^2$.