Question

A raindrop has a mass of 5.9e⁻⁷ kg and is falling near the surface of the Earth. Calculate the magnitude of the gravitational force exerted.

a) 5.9e⁻⁶ N
b) 5.9e⁻⁵ N
c) 5.9e⁻⁴ N
d) 5.9e⁻³ N

Answer 1

OPTION B.The magnitude of the gravitational force exerted on a raindrop with a mass of 5.9e⁻⁷ kg is calculated using the formula F = gm, leading to an answer of 5.9e⁻⁶ N.

Step-by-step explanation:

To calculate the magnitude of the gravitational force exerted on a raindrop with a mass of 5.9e⁻⁷ kg near the surface of the Earth, we use Newton's universal law of gravitation, which is stated as F = GMm/r². Here, F is the force of gravity, G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the mass of the Earth (approximately 5.98 × 10²⁴ kg), m is the mass of the object (the raindrop in this case), and r is the radius of the Earth (approximately 6.37 × 10⁶ m). The formula simplifies to F = gm when we are dealing with objects near the Earth's surface because the acceleration due to gravity, g, is about 9.81 m/s².

Substituting the known values, we get F = 5.9e⁻⁷ kg × 9.81 m/s² = 5.9e⁻⁷ kg × 9.81 N/kg = 5.79e⁻⁶ N. This value is approximately 5.9e⁻⁶ N, so the correct answer is a) 5.9e⁻⁶ N.