Question

$(based \: on \: gravitational \:intensity)$
↬At what distance from the centre of the moon the intensity of gravitational field will be zero take masses of earth and moon as
$5.98 \times {10}^{24} kg$
and
$7.35 \times {10}^{22} kg$
respectively distance between moon and Earth is
$3.85 \times {10}^{8}$


​

Answer 1

Answer:

• 3.85×10⁷ metres is the required answer.

Explanation:

According to the Question

It is given that ,

Mass of Earth = 5.98×10²⁴kg

Mass of Moon = 7.35×10²² Kg

Distance between of Earth & Moon = 3.85×10⁸m

We have to calculate the distance from the centre of the moon where the intensity of gravitational field will be zero .

As we know that gravitational force between two body is calculated by

• F = GMm/r²

Condition when the intensity of gravitational field will be zero when equal forces are applied by moon as well as Earth .

Now, let's calculate

Gravitational Field Intensity of Earth = Gravitational Field Intensity of Moon .

$\dashrightarrow\bf\; GE_{earth} = GE_{moon} \\\\\\\dashrightarrow\bf\; \frac{GM_e}{(d-x)^2} = \frac{GM_m}{(x)^2} \\\\\\\dashrightarrow\bf\; \frac{M_e}{(d-x)^2} = \frac{M_m}{(x)^2} \\\\\\\dashrightarrow\bf\; \frac{5.98\times10^{24}}{(d-x)^2} = \frac{7.35\times10^{22}}{(x)^2} \\\\\\\dashrightarrow\bf\; \frac{(x)^2}{(d-x)^2} = \frac{5.98\times10^{24}}{7.35\times10^{22}} \\\\\\\dashrightarrow\bf\; \frac{(x)^2}{(d-x)^2} = \cancel\frac{5.98\times10^{24}}{7.35\times10^{22}}$

$\dashrightarrow\bf\; \frac{(x)^2}{(d-x)^2} = \frac{59.8\times10^2}{7.35} \\\\\\\dashrightarrow\bf\; \frac{x}{d-x} = \sqrt{ \frac{59.8\times10^2}{7.35}} \\\\\\\dashrightarrow\bf\; \frac{x}{d-x} = 9\\\\\\\dashrightarrow\bf\; d-x= \frac{x}{9} \\\\\\\dashrightarrow\bf\; 3.85\times10^8 = \frac{x}{9} +x\\\\\\\dashrightarrow\bf\; 3.85\times10^8 \times\;9 = 10x\\\\\\\dashrightarrow\bf\; x = \frac{3.85\times10^8 \times9}{10} \\\\\\\dashrightarrow\bf\; x = 3.46\times10^8$

$\dashrightarrow\bf\; Distance \;from\; moon = 3.85\times10^8 - 3.46\times 10^8 \\\\\\\dashrightarrow\bf\; Distance \;from\; moon = 3.85\times10^7 m \; (approx)$$\bf\boxed{\sf\therefore \; The\; distance \;from\; the\; centre\; of \; the\; moon\; where\; gravitational \; field\; zero \; is\; 3.85\times10^7 metres. }$

Answer 2

Answer:

3.85×10⁷ metres is the required answer.

Explanation:

According to the Question

It is given that ,

Mass of Earth = 5.98×10²⁴kg

Mass of Moon = 7.35×10²² Kg

Distance between of Earth & Moon = 3.85×10⁸m

We have to calculate the distance from the centre of the moon where the intensity of gravitational field will be zero .

As we know that gravitational force between two body is calculated by

• F = GMm/r²

Condition when the intensity of gravitational field will be zero when equal forces are applied by moon as well as Earth .

Now, let's calculate

Gravitational Field Intensity of Earth = Gravitational Field Intensity of Moon .

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