Question

1. gravitational field strength is given by the formula: a) g = gm/r² b) g = mv²/r c) g = f/m² d) g = g/r²

Explanation:

To determine the formula for gravitational field strength, we recall the concept from physics. The gravitational field strength \( g \) at a distance \( r \) from a mass \( M \) is derived from Newton's law of gravitation \( F = \frac{GMm}{r^2} \), where \( G \) is the gravitational constant. Dividing both sides by the test mass \( m \) (since gravitational field strength is force per unit mass), we get \( g=\frac{GM}{r^2} \).

• Option B: \( g = \frac{mv^2}{r} \) is the formula for centripetal acceleration, not gravitational field strength.
• Option C: The correct formula for gravitational field strength in terms of force is \( g=\frac{F}{m} \) (not \( m^2 \)), so this is incorrect.
• Option D: The formula is missing the mass \( M \) of the object creating the gravitational field, so it is incorrect.

Answer:

A) \( g = \frac{GM}{r^2} \)