Question

Determine the value of the gravitational field at the surface of Earth if the gravitational field around an object of mass m is given by Fg / m (Fg is the gravitational force on the object due to Earth).

Answer 1

Answer:

Explanation:

The gravitational force on an object of mass m at a distance R from the earth's centre is given by

$F_g=G\frac{mM_E}{R^2}$

The gravitational field at a point at a distance R away from the centre of the earth is given by

$\vec{F}=\frac{F_g}{m}$

which in our case gives

$\vec{F}=\frac{F_g}{m}=G\frac{mM_E}{R^2}\cdot\frac{1}{m}$$\boxed{\vec{F}=G\frac{M_E}{R^2}\text{.}}$

Now at the surface of the earth R = 6371 *1000 m and

G = 6.67 * 10^-11

M_E = 5.97 * 10^24 kg

Therefore, the above formula gives

$\vec{F}=(6.67\cdot10^{-11})\frac{(5.97\cdot10^{24})}{(6371\cdot1000)^2}$

which upon evaluating gives us

$\boxed{\vec{F}=9.81N/kg\text{.}}$

which is our answer!