Question

A 2.0-kilogram mass is located 3.0 meters above
the surface of Earth. What is the magnitude of
Earth’s gravitational field strength at this
location?
(1) 4.9 N/kg (3) 9.8 N/kg
(2) 2.0 N/kg (4) 20. N/kg

Answer 1

(3) 9.8 N/kg is your answer.

Answer 2

The correct answer is: Option (3) 9.8 N/kg

Explanation:

According to Newton's Law of Gravitation:

$F_g = \frac{GmM}{R^2}$ --- (1)

Where G = Gravitational constant = 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²

m = Mass of the body = 2 kg

M = Mass of the Earth = 5.972 × 10²⁴ kg

R = Distance of the object from the center of the Earth = Radius of the Earth + Object's distance from the surface of the Earth = (6371 * 10³) + 3.0 = 6371003 m

Plug in the values in (1):

(1)=> $F_g = \frac{6.67408 * 10^{-11} * 2 * 5.972*10^{24}}{(6371003)^2} = 19.63$

Now that we have force strength at the location, we can use:

Force = mass * gravitational-field-strength

Plug in the values:

19.63 = 2.0 * gravitational-field-strength

gravitational-field-strength = 19.63/2 = 9.82 N/kg

Hence the correct answer is Option (3) 9.8 N/kg