5.4.2 Gravitational Potential

• The negative value of gravitational potential reflects gravity's attractive nature.


  True
• In the gravitational potential formula, \(G\) represents the gravitational constant.
• The gravitational potential formula is \(V = -\frac{GM}{r}\), where \(r\) is the distance from the center of the object.
• The gravitational constant is approximately \(6.67 \times 10^{-11} \, \text{Nm}^2\text{/kg}^2\)

  True
• Gravitational potential is defined as the work done per unit mass to bring an object from infinity to a given point
• Gravitational potential varies inversely with the distance
• The gravitational constant \(G\) is approximately 6.67 \times 10^{-11} \, \text{Nm}^2\text{/kg}^2
• In the gravitational potential formula, \(r\) represents the distance from the center of the object to the point where the potential is being measured
• What is the gravitational potential defined as in physics?

  Work done per unit mass
• The units of gravitational potential are J/kg
• Gravitational potential is measured in Joules per kilogram.

  True
• What are the units of gravitational potential?

  Joules per kilogram (J/kg)
• What is the gravitational potential at the surface of the Earth, given its mass and radius?

  \(-6.25 \times 10^7 \, \text{J/kg}\)
• What is the equation for gravitational force between two masses?

  $F =$$\frac{GMm}{r^{2}}$
• Why is gravitational potential always negative?

  Gravity is attractive
• The gravitational potential (\(V\)) can be calculated using the formula: V = -\frac{GM}{r}
• What is the gravitational potential at the Earth's surface in J/kg?

  $- 6.25 \times 10^{7} \, \text{J / kg}$
• The work done to move an object of mass \(m\) from a distance \(x\) to \(x + dx\) is \(dW = F dx
• Gravitational potential is always negative and varies inversely with distance from the mass.


  True
• What is the equation for escape velocity?

  $v =$$\sqrt{\frac{2GM}{r}}$
• What is the definition of gravitational potential?

  Work done per unit mass
• What is the formula for gravitational potential?

  $V =$$- \frac{GM}{r}$
• Why is gravitational potential always negative?

  Gravity attracts objects
• The formula to calculate gravitational potential (\(V\)) is -\frac{GM}{r}
• Steps in deriving the equation for gravitational potential

  1️⃣ Calculate the work done to move an object from \(x\) to \(x + dx\)

  2️⃣ Substitute the gravitational force \(F\)

  3️⃣ Integrate from infinity to \(r\)

  4️⃣ Divide by mass to find \(V\)
• Gravitational potential is always positive.

  False
• Match the terms with their definitions:

  G ↔️ Gravitational constant

  M ↔️ Mass of the object creating the field

  r ↔️ Distance from the object's center
• What is the value of the gravitational constant (\(G\)) in SI units?

  $6.67 \times 10^{ - 11} \, \text{Nm}^{2}\text{ / kg}^{2}$
• The units of gravitational potential are Joules per kilogram (J/kg).


  True
• What is the equation for gravitational potential (\(V\))?

  $V =$$- \frac{GM}{r}$
• Gravitational potential varies inversely with the distance from the mass.
• Suppose a satellite orbits Earth at 800 km above the surface. The orbital velocity is approximately 7450 m/s.
• Calculate the gravitational potential at a distance of 10 km from a celestial body with mass \(1.0 \times 10^{24}\) kg.

  $- 6.67 \times 10^{9} \, \text{J / kg}$
• What is the equation for satellite trajectory velocity?

  $v =$$\sqrt{\frac{GM}{r}}$
• What is the escape velocity from Earth's surface in m/s?

  $11200 \, \text{m / s}$