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Chapter 8: Problem 18

If the mass of a body on the surface of moon is denoted by \(\mathrm{M}_{\mathrm{m}}\) and that on the earth by \(\mathrm{M}_{e}\), then (1) \(\mathrm{M}_{\mathrm{m}}=\frac{\mathrm{M}_{\mathrm{e}}}{6}\) (2) \(\quad \mathrm{M}_{\mathrm{m}}=6 \mathrm{M}_{\mathrm{c}}\) (3) \(\mathrm{M}_{\mathrm{m}}=\frac{\mathrm{Me}}{2}\) (4) \(\mathrm{M}_{\mathrm{m}}=\mathrm{M}_{\mathrm{e}}\)

Short Answer

Expert verified
Answer: Mm = 6 × Me

Step by step solution

01

Recall the weight formula

Weight is the force with which a body is attracted towards the center of the Earth (or any other celestial body), and is given by: Weight = mass × gravitational acceleration (g)
02

Define the given variables

Let Mm be the mass of a body on the moon and Me be the mass on Earth. The gravitational acceleration on Earth (ge) is 9.81 m/s², and on the moon (gm), it is 1.625 m/s². We also know that the weight of the body must be the same on both Earth and the moon.
03

Set up the weight equation

Since the weight is the same on both Earth and the moon, we can set up the following equation: Weight on Earth = Weight on Moon Me × ge = Mm × gm
04

Solve for the mass on the moon

Now we'll solve the equation for Mm in terms of Me: Me × ge = Mm × gm Mm = (Me × ge) / gm Plug in the values for ge and gm: Mm = (Me × 9.81) / 1.625
05

Simplify the equation

To simplify the equation further, we can divide both the numerator and denominator by the common factor 1.625: Mm = (Me × 6) / 1 Now the equation becomes: Mm = 6 × Me
06

Match the result with the given options

Comparing the result with the given options, we find that it matches option (2): Mm = 6 × Me Hence, the correct answer is option (2).

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