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The weight of a man on the surface of the earth is 392 N. Find its mass $(Take g_{e} = 9.8 {ms}^{- 2}$ . If the man were taken to the moon, what would be his mass and weight? Calculate the acceleration due to gravity on the moon?

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40 kg, 40 kg, 65.3 N and 1.63

{ms}^{- 2}

50 kg, 50 kg, 45.3 N and 2.63

{ms}^{- 2}

50 kg, 40 kg, 55.3 N and 2.89

{ms}^{- 2}

60 kg, 50 kg, 65.3 N and 3.46

{ms}^{- 2}

answer is A.

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Detailed Solution

Given that, Acceleration due to gravity on the earth,

g_{e}

= 9.8

{ms}^{- 2}

Weight of a man on the earth,

W_{e}

= 392 N
Hence, Mass of a man on the earth, m =

\frac{W_{e}}{g_{e}}

⸫ m =

\frac{392}{9.8}

= 40 kg
Thus, Mass of the man on the earth = Mass of the man on the moon = m = 40 kg
We know that weight on the moon is

\frac{1}{6}

th of its weight on the earth
Then, weight of the object on the moon,

W_{m}

\frac{1}{6}

W_{e}

\frac{1}{6} \times 392

⸫

W_{m}

= 65.3 N
We know that acceleration due to gravity on the moon,

g_{m} =

\frac{W_{e}}{W_{m}}

\frac{{m \times g}_{e}}{{m \times g}_{m}}

g_{m}

\frac{65.3 \times 9.8}{392}

= 1.63

{ms}^{- 2}

So, mass of a man on the earth and the moon is 40 kg, its weight on the surface of moon will be 65.3 N and acceleration due to gravity on the moon will be 1.63

{ms}^{- 2}

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