Question

A 2 kg object is a distance of 10,000,000 m away from the center of Earth, which has a mass of nearly 6×1024 kg. What is the approximate gravitational field strength of Earth’s gravitational field at the location of the 10 kg object?


A2 N/kg

B 4 N/kg

C 10 N/kg

D The gravitational field strength is negligible and, therefore, approximately zero.

Answer 1

Answer:

4 (N/kg) or B

Explanation:

An application of the equation for Newton’s law of universal gravitation can be used to determine the gravitational field strength at the 2 kg object’s location.

Answer 2

The approximate gravitational field strength of Earth’s gravitational field at the location of the 10 kg object is 4.00 N/kg. Hence, option (B) is correct.

Given data:

The mass of object is, $m = 2\;\rm kg$.

The distance of object from Earth is, $d=10,000,000\;\rm m$.

The mass of Earth is, $M=6 \times 10^{24} \;\rm kg$.

The expression for the gravitational field strength of Earth is,

$g = \dfrac{GM}{d^{2}}$

Here, G is the universal gravitational constant and its standard value is $6.67\times10 ^{-11} \;\rm Nm^{2}/kg^{2}$.

Solve by substituting the values as,

$g = \dfrac{6.67 \times 10^{-11} \times 6 \times 10^{24}}{(10,000,000)^{2}}\\g \approx 4.00 \;\rm N/kg$

Thus, we can conclude that approximate value of gravitational field strength of Earth at the location of object is 4.00 N/kg. And option (B) is correct.

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