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Calculate the value of acceleration due to gravity on the surface of the moon.

(Given Mass of the moon $=7.4 \times 10^{22} \mathrm{~kg} ;$ Radius of moon $\left.=1740 \mathrm{~km} ; G=6.7 \times 10^{-11} \mathrm{Nm}^{2}/\mathrm{kg}^{2}\right)$

Solution

The formula for calculating the acceleration due to gravity is :
$$g=G \times \frac{M}{R^{2}}$$

Here, Gravitational constant :

$G=6.7 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$

Mass of the moon, $M=7.4 \times 10^{22} \mathrm{~kg}$

Radius of the moon, $R=1740 \mathrm{~km}$
$$\begin{array}{l} =1740 \times 1000 \mathrm{~m} \\ =1.74 \times 10^{6} \mathrm{~m} \end{array}$$

Now, putting these values of $G, M$ and $R$ in the above formula, we get:
$$g=\frac{6.7 \times 10^{-11} \times 7.4 \times 10^{22}}{\left(1.74 \times 10^{6}\right)^{2}}$$

$$\text { or } \quad g=1.63 \mathrm{~m} / \mathrm{s}^{2}$$

Thus, the acceleration due to gravity, $g$, on the surface of the moon is $1.63 \mathrm{~m} / \mathrm{s}$

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