Calculate the gravitation force of attraction between two planets of $10^{24}$kg and $10^{27}$kg separated by a distance of $10^{20}$meters

Analyze the question: We need the gravitational force between two masses using Newton's law of universal gravitation.

Concept: F = G m₁m₂ / r²

where G = 6.67 × 10⁻¹¹ N m² kg⁻², m₁ and m₂ are the masses, and r is the distance between their centres.

Solution:

m₁ = 10²⁴ kg, m₂ = 10²⁷ kg, r = 10²⁰ m

1. Product of masses: m₁m₂ = 10²⁴ × 10²⁷ = 10⁵¹
2. Distance squared: r² = (10²⁰)² = 10⁴⁰
3. Substitute:

F = (6.67 × 10⁻¹¹ × 10⁵¹) / 10⁴⁰

4. Combine the powers of 10: 10⁻¹¹ × 10⁵¹ = 10⁴⁰, and 10⁴⁰ / 10⁴⁰ = 1

F = 6.67 × 1 = 6.67 N

Answer: A (6.67 N)

Tip: In questions like this, the powers of 10 often cancel neatly. Add the exponents on top (24 + 27 = 51), subtract the exponent below (2 × 20 = 40), then include G's exponent (-11): 51 - 40 - 11 = 0. So the answer is just the value of G, 6.67. When you see the exponent working out to zero, you know the answer is the digit part of G. This saves time in the exam hall.