Question

A body has a weight 90 kilo gram on the surface of the earth the mass of the moon is 1/ 9 that of Earth's mass and its radius is 1 /2that of the earth's radius on the Moon the weight of the body is

Answer 1

Answer on Question 78088, Physics, Astronomy, Astrophysics

Question:

A body has a weight $90\,kg$ on the surface of the Earth, the mass of the Moon is $1/9$ that of Earth's mass and its radius is $1/2$ that of the Earth's radius. On the Moon the weight of the body is?

Solution:

As we know, the acceleration due to gravity on the surface of the Earth is given by the formula:

$$g_E = \frac{G M_E}{R_E^2},$$

here, $G$ is the universal gravitational constant, $M_E$ is the mass of the Earth, $R_E$ is the radius of the Earth.

Then, from the definition of the weight, we can find the weight of the body on the Earth:

$$W_E = m \frac{G M_E}{R_E^2} = m g_E,$$

here, $m$ is the mass of the body.

Also, we know from the condition of the question that $M_M = \frac{1}{9} M_E$, $R_M = \frac{1}{2} R_E$.

Then, the acceleration due to gravity on the surface of the Moon will be:

$$g_M = \frac{G \frac{1}{9} M}{\left(\frac{1}{2} R\right)^2} = \frac{4}{9} \frac{G M}{R^2} = \frac{4}{9} g_E.$$

Then, the weight of the body on the Moon:

$$W_M = m \frac{4}{9} g_E .$$

Let's divide equation (2) by equation (1), we get:

$$\frac{W_M}{W_E} = \frac{m \frac{4}{9} g_E}{m g_E} = \frac{4}{9}.$$

Then, we can find the weight of the body on the Moon:

$$W _ {M} = \frac {4}{9} \cdot W _ {E} = \frac {4}{9} \cdot 90 \text{ kg} = 40 \text{ kg}.$$

Answer:

$$W _ {M} = 40 \text{ kg}.$$

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