Question

Masses of the earth and the moon are in the ratio of 3:2 and radii of the earth and the moon are in the ratio of 6:1 . The ratio of the weight of the body of their surfaces will be ?

Answer 1

Given :

The ratio of masses of moon and earth = 3:2

The ratio of radii of moon and earth = 6:1

To Find :

The ratio of weight of the bodies on their surfaces = ?

Solution :

• The weight of the body depends on the acceleration due to gravity on the surface of the planet

             W=mg

• The acceleration due to gravity is given by the formula  $g=\frac{GM}{R^{2} }$

• The weight of the body is given by     $W=m\times \frac{GM}{R^{2} }$

          $W_{1} =m\times \frac{GM_{1} }{R_{1} ^{2} } \rightarrow Equation(1)$

          $W_{2} =m\times \frac{GM_{2} }{R_{2} ^{2} } \rightarrow Equation(2)$

         $\frac{W_{1} }{W_{2} } = \frac{M_{1} }{M_{2} } \times \frac{R_{2} ^{2} }{R_{1} ^{2} }$

         $\frac{W_{1} }{W_{2} } = \frac{3}{2 } \times \frac{1 }{36}$

         $\frac{W_{1} }{W_{2} } =\frac{1}{24}$

• The ratio of weights on their surfaces is 1:24

         

Answer 2

The ratio of the weight of the body of their surfaces is 1 : 24

Explanation:

The weight of the body is given by the formula:

W = mg

Where,

g = Acceleration due to gravity

The acceleration due to gravity is given by the formula:

g = GM/r²

Where,

r = Radius of the planet

G = Gravitational constant

M = Mass of the planet

The weight of the body in earth is:

We = m × G(Me)/(re)²

The weight of the body in moon is:

Wm = m × G(Mm)/(rm)²

The ratio of weight is given as:

We/Wm = (m × G(Me)/(re)²)/(m × G(Mm)/(rm)²)

We/Wm = ((Me)/(re)²)/((Mm)/(rm)²)

We/Wm = 3/36 × 1/2

∴ We/Wm = 1/24