Question

On what factors does the value of g depend?

Answer 1

The acceleration due to gravity is given by,

g=GMR2g =G\frac{M}{R^2}$g=\frac{GM}{R^2}$

$M$ the mass of the planet and

$R$ is the distance of the point under consideration from the centre of the planet.

(i) due to height above or below the surface of planet,

$g^{\prime }=g{(1+\frac{h}{R})}^{-2},wherehisheightabovethesurfaceoftheplanet$

$g^{\prime }=g(1-\frac{h}{R}),wherehisdepthbelowthesurfaceoftheplanet$

(ii) Due to shape of planet, as it bulges out of the equator and flat on poles.

$R_e>R_p\cong 21km$

$\therefore g_p>g_e$

(iii) Due to rotation of the planet

$g^{\prime }=g_p-r{\omega }^{2}co{s}^2\lambda$

Therefore, acceleration due to gravity ($g$) depends on the mass of the planet, distance between centre of planet and object, shape of the planet, rotational parameters of the planet.