Two objects P and Q of masses 100kg and 20kg respectively are 1.2m apart on a horizontal surface. Calculate…

Analyze the question: Two masses attract each other with gravitational force. We need the force on Q due to P, and its direction.

Concept: Newton's law of universal gravitation:

F = G·m₁·m₂ / r²

The force is always attractive, so the force on Q points toward P.

Solution:

• m₁ = 100 kg, m₂ = 20 kg, r = 1.2 m
• G = 6.67 × 10⁻¹¹ N m² kg⁻²

F = (6.67 × 10⁻¹¹ × 100 × 20) / (1.2)²

Numerator: 6.67 × 10⁻¹¹ × 2000 = 1.334 × 10⁻⁷

Denominator: 1.44

F = 1.334 × 10⁻⁷ / 1.44 = 9.26 × 10⁻⁸ N

Direction: Gravity is attractive, so Q is pulled toward P.

Check against options: A and B (1.11 × 10⁻⁷ N) would come from using r = 1.2 without squaring correctly or another slip, so they don't match. D has the right magnitude but the wrong direction, since the force on Q cannot be toward Q itself. Option C matches both magnitude and direction.

Answer: C. 9.26 × 10⁻⁸ N towards P

Exam tip: Always square the distance, and remember that "force on X" in gravity always points toward the other object. Quickly eliminate options with a direction that points back to the object itself.