What is the gravitational field strength at a distance of 3R from the center of
Practice Questions
Q1
What is the gravitational field strength at a distance of 3R from the center of a planet of radius R?
G/9
G/3
G
3G
Questions & Step-by-Step Solutions
What is the gravitational field strength at a distance of 3R from the center of a planet of radius R?
Step 1: Understand the formula for gravitational field strength, which is g = GM/r², where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet.
Step 2: Identify the distance from the center of the planet. In this case, the distance is 3R, where R is the radius of the planet.
Step 3: Substitute the distance into the formula. Replace r with 3R in the formula: g = GM/(3R)².
Step 4: Calculate (3R)². This equals 9R².
Step 5: Substitute 9R² back into the formula: g = GM/(9R²).
Step 6: Simplify the equation. This gives g = (GM/R²) * (1/9).
Step 7: Recognize that GM/R² is the gravitational field strength at the surface of the planet, which we can denote as g_surface. Therefore, g = g_surface / 9.
