Answered

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

Verified Answer :

PhyCS

(3) 9.8 N/kg is your answer.

IsrarAwan

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

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