Example Universal Gravitation (Finding distance)
A sphere of mass 40 kg is attracted by a second sphere of mass 60 kg with a force equal to 4 mgf. If G = 6×10⁻¹¹ N·m²·kg⁻² and g = 10 m·s⁻², find the distance between them.
M = 40 kg, m = 60 kg, G = 6×10⁻¹¹ N·m²·kg⁻², g = 10 m·s⁻²
Force given: F = 4 mgf (here mgf = (10⁻⁶ kg)·g)
F = 4×(10⁻⁶ kg)×(10 m·s⁻²) = 4×10⁻⁵ N
Distance r between the spheres (in metres).
Newton’s law of gravitation: F = (G M m) / r²
Rearranging: r = √(G M m / F)
r = √[(6×10⁻¹¹ × 40 × 60) / (4×10⁻⁵)]
r = √(3.6×10⁻³) = 0.060 m
Answer: r = 0.060 m = 6.0 cm
Tip: Always keep r in metres in the final SI answer. Convert to cm only as an additional step.
Student Details
Worksheet 6 Similar Questions (Attempt first, then Submit)
Two spheres of masses 20 kg and 50 kg attract each other with force F = 1.0×10⁻⁶ N. Take G = 6.67×10⁻¹¹ N·m²·kg⁻². Find the distance r between them.
Two spheres each of mass 10 kg are separated by 0.50 m. Using G = 6.67×10⁻¹¹ (SI), find the gravitational force between them.
A mass m = 5.0 kg is at a distance r = 0.20 m from another mass M = 30 kg. Take G = 6.67×10⁻¹¹ (SI). Find the force of attraction.
Two masses M = 80 kg and m = 20 kg attract with force F = 5.0×10⁻⁷ N. Take G = 6.67×10⁻¹¹ (SI). Find their separation r.
At what distance from a 60 kg mass will the gravitational field (acceleration due to that mass) be g = 1.0×10⁻⁸ m·s⁻²? Take G = 6.67×10⁻¹¹ (SI). (Use g = GM/r².)
Two masses 40 kg and 60 kg are placed 0.30 m apart. Find the gravitational force between them using G = 6.67×10⁻¹¹ (SI).
Answer Key (shown after Submit)
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After Submit, compare your final SI answer and your substitution steps. If your magnitude differs, recheck powers of 10 and unit conversions.