What is the gravitational field strength at a distance of 3R from the center of a planet of mass M and radius R?
Practice Questions
1 question
Q1
What is the gravitational field strength at a distance of 3R from the center of a planet of mass M and radius R?
G*M/R²
G*M/(3R)²
G*M/(9R²)
G*M/(6R²)
g = GM/r², at 3R, g = GM/(3R)² = GM/9R².
Questions & Step-by-step Solutions
1 item
Q
Q: What is the gravitational field strength at a distance of 3R from the center of a planet of mass M and radius R?
Solution: g = GM/r², at 3R, g = GM/(3R)² = GM/9R².
Steps: 6
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: The final expression for gravitational field strength at a distance of 3R from the center of the planet is g = GM/9R².
