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Q.

What is the ratio of the weight of a body on the moon to the weight of the same body on the earth?

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a

1 / 8

b

1 / 6

c

1 / 12

d

1 / 3

answer is B.

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Detailed Solution

The ratio of the weight of a body on the moon to the weight of the same body on the earth is

1 / 6

.
Weight is defined as the force of gravity with which a body is attracted to the earth or another celestial body, and it is equal to the product of the object's mass, and the acceleration due to gravity of the celestial body of the planet.
Given data and assumptions:
Weight of the object on the earth,

= W_{e}

Weight of the same object on the moon,

= W_{m}

Acceleration due to gravity of the earth,

= g_{e}

Acceleration due to gravity of the moon,

= g_{m}

We know tha weight is defined mathematically as,

W = m \times g

\frac{W_{e}}{W_{m}} = \frac{m \times g_{e}}{m \times g_{m}}

……..(i)
We know that the acceleration due to gravity of the moon is

1 / 6

th of the acceleration due to gravity of the earth. Mathematically,

g_{m} = \frac{1}{6} \times g_{e}

Putting it in eqn(i)

\frac{W_{e}}{W_{m}} = \frac{m \times g_{e} \times 6}{m \times g_{e}}

\frac{W_{e}}{W_{m}} = \frac{6}{1}

\frac{W_{m}}{W_{e}} = \frac{1}{6}

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