Question

Find the expression for acceleration due to gravity 'g' for a planet of mass M and radius R​

Answer 1

Formula of Acceleration due to Gravity

Force acting on a body due to gravity is given by, f = mg

Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body.

According to the universal law of gravitation, f = GmM/(r+h)2

Where,

f = force between two bodies,

G = universal gravitational constant (6.67×10-11 Nm2/kg2)

m = mass of the object,

M = mass of the earth,

r = radius of the earth.

h = height at which the body is from the surface of the earth.

As the height (h) is negligibly small compared to the radius of the earth we re-frame the equation as follows,

f = GmM/r2

Now equating both the expressions,

mg = GmM/r2

⇒ g = GM/r2

Therefore, the formula of acceleration due to gravity is given by, g = GM/r2

BTS AND EXO

Answer 2

$\large\boxed{\rm { F = mg}}$ where 'm' is the mass, 'g' is acceleration due to gravity.

$\large\rm { F = \frac {G \cdot M × m}{d^{2}}}$

$\large\rm { mg = \frac { G \cdot M × m}{d^{2}}}$

$\large\boxed{\rm { g = G \frac {M}{d^{2}}}}$

Where 'M' is mass of earth and 'd' is distance between object and Earth.

• if object is on or near earth then distance = radius .

$\large\rm { so \ , g = \frac {G×M}{R^{2}}}$