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The value of acceleration due to gravity on the moon as compared to that on the earth is

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Half

One-sixth

One-eighth

One-tenth

answer is B.

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Detailed Solution

The value of acceleration due to gravity on the moon as compared to that on the earth is one-sixth.
The earth's mass is approximately

100

times that of the moon, and its radius is

4

times that of the moon.
Assumptions:
The mass of the earth,

m_{earth} = 100 \times m_{moon}

The radius of the earth,

{r^{}}_{earth} = 4 \times {r^{}}_{moon}

\Rightarrow

g_{moon} = \frac{G m_{moon}}{{r^{2}}_{moon}}

\Rightarrow

g_{earth} = \frac{G m_{earth}}{{r^{2}}_{earth}}

So,

\frac{g_{moon}}{g_{earth}} = \frac{\frac{G m_{moon}}{{r^{2}}_{moon}}}{\frac{G m_{earth}}{{r^{2}}_{earth}}}

\Rightarrow

\frac{g_{moon}}{g_{earth}} = \frac{m_{moon} \times {r^{2}}_{earth}}{m_{earth} \times {r^{2}}_{moon}}

\Rightarrow

\frac{g_{moon}}{g_{earth}} = \frac{m_{moon} \times (4 \times {r^{}}_{moon})^{2}}{100 \times m_{moon} \times {r^{2}}_{moon}}

\Rightarrow \frac{g_{moon}}{g_{earth}} = \frac{16}{100}

\Rightarrow

\frac{g_{moon}}{g_{earth}} = \frac{1}{6}

\Rightarrow

g_{moon} = \frac{1}{6} \times g_{earth}

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