The mass of the earth is 6.0 x 1024kg and that of the moon is 7.0 x 1022kg. If the distance between them is…

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

Concept: F = G·M·m / r²

Solution:

Given: M = 6.0 × 10²⁴ kg, m = 7.0 × 10²² kg, r = 4.0 × 10⁸ m, G = 6.7 × 10⁻¹¹ N m² kg⁻²

(The question shows the powers without superscripts, so I have read them as 10²⁴, 10²², 10⁸ and 10⁻¹¹.)

1. Numerator: G·M·m = 6.7 × 10⁻¹¹ × 6.0 × 10²⁴ × 7.0 × 10²² • 6.7 × 6.0 × 7.0 = 281.4 • Powers of 10: −11 + 24 + 22 = 35 • So the numerator = 281.4 × 10³⁵ = 2.814 × 10³⁷

2. Denominator: r² = (4.0 × 10⁸)² = 16 × 10¹⁶ = 1.6 × 10¹⁷

3. Divide: F = (2.814 × 10³⁷) / (1.6 × 10¹⁷) F ≈ 1.76 × 10²⁰ N ≈ 1.8 × 10²⁰ N

Answer: Option D, 1.8 × 10²⁰ N.

Tip: In gravitation problems, handle the numbers and the powers of 10 separately. Add the exponents in the numerator, then subtract the exponent of the denominator (here 37 − 17 = 20). Always remember to square the distance. Most mistakes come from forgetting this step.