Question on: JAMB Physics - 2024
The gravitational force between two objects masses 10\(^{24}\)kg and 10\(^{27}\)kg is 6.67N. Calculate the distance between them [ G = 6.6 x 10\(^{-11}\)Nm\(^2\)kg\(^{-2}\) ]
1.0 x 10\(^{20}\)m
2.0 x 10\(^{-20}\)m
1.0 x 10\(^{-20}\)m
2.0 x 10\(^{20}\)m
The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force (6.67 N)
- G is the gravitational constant (6.6 x 10-11 Nm²kg⁻²)
- m1 and m2 are the masses of the objects (1024 kg and 1027 kg)
- r is the distance between the centers of the objects (what we need to find)
1. Rearrange the formula to solve for r:
r = sqrt[ G * (m1 * m2) / F ]
2. Substitute the given values:
r = sqrt[ (6.6 x 10-11) * (1024 * 1027) / 6.67 ]
3. Simplify the expression:
r ≈ sqrt[ 1040 ]
r = 1.0 x 1020 m
Therefore, the distance between the two objects is approximately 1.0 x 1020 m.
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