Solved Examples of Gravitational Field Strength Calculations

📚 Quick Study Guide

• 🌍 Gravitational field strength ($g$) is the force per unit mass experienced by a small test mass placed in the field.
• 🔢 Formula: $g = \frac{F}{m}$, where $F$ is the gravitational force and $m$ is the mass.
• 📏 Units: Measured in Newtons per kilogram (N/kg) or meters per second squared (m/s²).
• 🍎 Near the Earth's surface, $g \approx 9.81 \,\text{N/kg}$.
• 🚀 For a point mass $M$, $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant ($6.674 × 10^{-11} \,\text{N m}^2\text{/kg}^2$) and $r$ is the distance from the mass.
• 💡 Gravitational field strength is a vector quantity; it has both magnitude and direction (always pointing towards the mass creating the field).

🧪 Practice Quiz

1. What is the gravitational field strength at a point where a 5 kg mass experiences a gravitational force of 25 N?
   1. 5 N/kg
   2. 20 N/kg
   3. 30 N/kg
   4. 125 N/kg
2. A satellite of mass 500 kg orbits the Earth at a distance where the gravitational field strength is 4 N/kg. What is the gravitational force acting on the satellite?
   1. 200 N
   2. 125 N
   3. 2000 N
   4. 4 N
3. The gravitational field strength due to a planet at a certain distance is 8 N/kg. If the distance is doubled, what will be the new gravitational field strength?
   1. 2 N/kg
   2. 4 N/kg
   3. 16 N/kg
   4. 32 N/kg
4. What is the gravitational field strength at the surface of a planet with mass $6 × 10^{24}$ kg and radius $6.4 × 10^6$ m? (Given: $G = 6.674 × 10^{-11} \,\text{N m}^2\text{/kg}^2$)
   1. 5.8 N/kg
   2. 9.8 N/kg
   3. 12.6 N/kg
   4. 16.3 N/kg
5. A 2 kg object is placed in a gravitational field with a strength of 10 N/kg. What is the weight of the object?
   1. 5 N
   2. 10 N
   3. 12 N
   4. 20 N
6. If the gravitational field strength on the Moon is 1.6 N/kg, what force would a 10 kg object experience on the Moon?
   1. 1.6 N
   2. 6.25 N
   3. 10 N
   4. 16 N
7. Two planets have the same mass, but planet A has twice the radius of planet B. What is the ratio of the gravitational field strength at the surface of planet A to that of planet B?
   1. 1:4
   2. 1:2
   3. 2:1
   4. 4:1