Question

(a) What do you understand by free fall? Derive an expression for acceleration due to gravity.
(b) Mass of earth is 81 times that of the moon, and its diameter is 3.6 times that of the moon. Compare the acceleration due to gravity on the earth and on the moon.

Answer 1

Explanation:

Acceleration due to gravity is the acceleration of a freely falling body. Free falling means to drop vertically with no air resistance and an acceleration that doesn't change, or that is constant. The symbol for acceleration due to gravity is the letter g. The acceleration due to gravity, g is directed towards the center of whatever object gravity is draw towards, for example Earth, or any other planet.

An equation can be used to find the gravitational acceleration in different places. This equation is …



G is a constant, called the universal gravitational constant, which is equal to 6.67 × 10−11 N·m2/kg2. M is the mass of the object in which gravitational acceleration is being found. R is the radius of the object. There is a negative sign in front of the equation because objects in free fall always fall downwards toward the center of the object.

The acceleration due to gravity is 1.62 m/s2. This is approximately 1/6 that of the acceleration due to gravity on Earth, 9.81 m/s2.

Answer 2

Explanation:

(a)When an objects falls freely under the influence of the gravity without air friction then free fall is defined.

Since we know that

$W =mg$.................(1)

Newton's law of gravitation is

$F = \dfrac{GMm}{R^{2} }$...................(2)

from (1) and (2) we get,

$g = \dfrac{GM}{R^{2}}$

(b)Since we know that the formula for acceleration due to gravity on earth is

$g = \dfrac{GM}{R^{2} }$................(1)

Where G =gravitaional constant,M=mass of the earth and R =radius of the earth.

Since it is given that Mass of earth is 81 times that of the moon, and its diameter is 3.6 times that of the moon.

So,acceleration due to gravity on moon is.

$g' = \dfrac{GM}{6.25R^{2} }$..................(2)