Question

What do you estimate the value of acceleration due to gravity to be close to the Earth? Why do you think it will be this value?

Answer 1

Explanation:

the value of acceleration due to gravity on the surface of the earth is

$g=9.8\text{ m/s}^2$

as we know, the gravity is related as,

$g=\frac{GM}{R^2}$

Here,

$G=6.67\times10^{-11}\text{ N m}^2\text{ /kg}^2$

is a Gravitational constant,

$m=5.972\times10^{24}\text{ kg}$

is the mass of the earth and

$R=6.371\times10^3\text{ Km}$

is the radius of the earth,

After plugging all the values in the above relation we get

$\begin{gathered} g=\frac{6.67\times10^{-11}Nm^2/kg^2\times5.972\times10^{24}kg}{6.371\times10^6\text{ m}}\text{ } \\ g\approx9.8\text{ m/s}^2 \end{gathered}$

Thus, we get acceleration due to gravity is

$9.8\text{ m/s}^2$