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Two bodies of masses $M$ and $m$ are separated by a distance $r$. According to Newton's law of gravitation, what is the nature of the force between them?
Two bodies of masses $M$ and $m$ are separated by a distance $r$. According to Newton's law of gravitation, what is the nature of the force between them?
- The force can be either attractive or repulsive depending on the medium between the bodies.
- The force is always repulsive, pushing the bodies away from each other.
- The force is attractive, pulling the bodies towards each other. (correct)
- There is no force between the bodies as long as they are stationary.
Two objects with masses $M$ and $m$ interact gravitationally. Which factor, when increased, would decrease the gravitational force between them?
Two objects with masses $M$ and $m$ interact gravitationally. Which factor, when increased, would decrease the gravitational force between them?
- The sum of the masses ($M + m$).
- The product of the masses ($M \times m$).
- The gravitational constant.
- The distance ($r$) separating their centers. (correct)
If the distance between two bodies is doubled, what happens to the gravitational force between them?
If the distance between two bodies is doubled, what happens to the gravitational force between them?
- It becomes four times the original force.
- It reduces to one-quarter of the original force. (correct)
- It doubles.
- It remains the same.
Consider two objects interacting gravitationally. If the mass of one object is doubled while the distance between them is also doubled, how does the gravitational force change?
Consider two objects interacting gravitationally. If the mass of one object is doubled while the distance between them is also doubled, how does the gravitational force change?
Two spheres of masses $m_1$ and $m_2$ are placed a distance $r$ apart. If $m_1$ is increased to $4m_1$ and $r$ is increased to $2r$, what is the new gravitational force between them?
Two spheres of masses $m_1$ and $m_2$ are placed a distance $r$ apart. If $m_1$ is increased to $4m_1$ and $r$ is increased to $2r$, what is the new gravitational force between them?
Two celestial bodies are separated by a distance, $r$. If the distance between them is doubled, how does the gravitational force, $F$, between them change?
Two celestial bodies are separated by a distance, $r$. If the distance between them is doubled, how does the gravitational force, $F$, between them change?
A hypothetical planet has a radius of $R$ and an acceleration due to gravity of $g$ at its surface. What is the escape velocity from this planet in terms of $R$ and $g$?
A hypothetical planet has a radius of $R$ and an acceleration due to gravity of $g$ at its surface. What is the escape velocity from this planet in terms of $R$ and $g$?
The mass of Earth is calculated using the formula derived from Newton's law of universal gravitation. If the measured radius of the Earth were smaller than the actual radius by a factor of two, how would this affect the calculated mass, assuming $g$ and $G$ are known and constant?
The mass of Earth is calculated using the formula derived from Newton's law of universal gravitation. If the measured radius of the Earth were smaller than the actual radius by a factor of two, how would this affect the calculated mass, assuming $g$ and $G$ are known and constant?
Two spheres of masses $m_1$ and $m_2$ are separated by a distance $r$. If the mass of each sphere is doubled, what happens to the gravitational force between them?
Two spheres of masses $m_1$ and $m_2$ are separated by a distance $r$. If the mass of each sphere is doubled, what happens to the gravitational force between them?
Consider two objects attracting each other gravitationally. If the gravitational constant, $G$, were suddenly doubled, while all other parameters (masses and distance) remained the same, what would happen to the gravitational force between them?
Consider two objects attracting each other gravitationally. If the gravitational constant, $G$, were suddenly doubled, while all other parameters (masses and distance) remained the same, what would happen to the gravitational force between them?
How does the gravitational force (F) between two masses change if the distance (r) between their centers is doubled?
How does the gravitational force (F) between two masses change if the distance (r) between their centers is doubled?
A planet has a mass M and a radius R. If the acceleration due to gravity on the planet's surface is g, which formula correctly expresses the mass of the planet?
A planet has a mass M and a radius R. If the acceleration due to gravity on the planet's surface is g, which formula correctly expresses the mass of the planet?
What happens to the escape velocity of a planet if both its mass and radius are doubled?
What happens to the escape velocity of a planet if both its mass and radius are doubled?
According to Kepler's Law of Periods, how does the period (T) of a planet's orbit relate to its average distance (r) from the Sun?
According to Kepler's Law of Periods, how does the period (T) of a planet's orbit relate to its average distance (r) from the Sun?
A spacecraft is launched from Earth. Which of the following changes would decrease the escape velocity required for the spacecraft?
A spacecraft is launched from Earth. Which of the following changes would decrease the escape velocity required for the spacecraft?
Planet X has a gravitational potential of V at its surface. What is the physical significance of the absolute value of the gravitational potential, |V|, in relation to escape velocity?
Planet X has a gravitational potential of V at its surface. What is the physical significance of the absolute value of the gravitational potential, |V|, in relation to escape velocity?
A planet orbits a star in an elliptical path. According to Kepler's Law of Areas, where does the planet move the fastest in its orbit?
A planet orbits a star in an elliptical path. According to Kepler's Law of Areas, where does the planet move the fastest in its orbit?
Two planets have the same radius, but Planet A has twice the mass of Planet B. How does the gravitational potential at the surface of Planet A compare to that of Planet B?
Two planets have the same radius, but Planet A has twice the mass of Planet B. How does the gravitational potential at the surface of Planet A compare to that of Planet B?
Flashcards
Gravitational Interaction
Gravitational Interaction
Force existing between two bodies with masses M and m separated by a distance r.
Newton's Law of Gravitation
Newton's Law of Gravitation
States that a force exists between interacting bodies.
Line of Action (Gravity)
Line of Action (Gravity)
The straight line joining the centers of two interacting masses.
Attractive Force (Gravity)
Attractive Force (Gravity)
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Distance 'r' in Gravitation
Distance 'r' in Gravitation
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Gravitational Force
Gravitational Force
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Formula for Gravitational Force
Formula for Gravitational Force
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Gravitational Potential (V)
Gravitational Potential (V)
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Formula for Gravitational Potential
Formula for Gravitational Potential
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Planet's mass (M)
Planet's mass (M)
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Escape Velocity (v)
Escape Velocity (v)
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Formula for Escape Velocity
Formula for Escape Velocity
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Kepler's Law of Orbits
Kepler's Law of Orbits
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Escape Velocity
Escape Velocity
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Value of Gravitational Constant (G)
Value of Gravitational Constant (G)
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Gravitational Force Calculation (Example)
Gravitational Force Calculation (Example)
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Escape Velocity Formula
Escape Velocity Formula
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Mass of the Earth (M)
Mass of the Earth (M)
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Study Notes
- If there are two bodies of masses M and m whose centers are separated by a distance r, they exert a force of interaction on each other, which can be attractive or repulsive.
- This force acts along the common centers of the bodies
Newton's Law of Gravitation
- Defines the force between two interacting bodies: F = G (Mm / r^2)
- F is measured in Newtons (N)
- The relationship F ∝ 1/r^2 is an inverse-square law
- F represents the force between the interacting masses (in N)
- r is the distance between the centers of the masses (in m)
- G is the universal gravitational constant (G = 6.67 × 10^-11 Nm^2kg^-2)
Gravitational Potential (V)
- Formula: V = -GM/r or V = -gr
- Measured in Nmkg^-1
- M is the mass of the planet in kg
- r is the radius of the planet in m
- g is the acceleration due to gravity on the planet in ms^-2
Mass M of a Planet
- Can be calculated using: M = gR^2/G
- Where all the parameters maintain their meanings
Escape Velocity (v)
- Formula: v = √(2GM/r) or v = √(2gr) or v = √(2|V|)
- |V| is the magnitude of the gravitational potential in Nmkg^-1
- M is the mass of the planet in kg
- r is the radius of the planet in m
Kepler's Laws of Planetary Motion
Law of Orbits
- Each planet moves in an elliptical orbit with the Sun at one focus of the ellipse
Law of Areas
- A line joining the Sun to a given planet sweeps out equal areas in equal times
Law of Periods
- The squares of the periods of revolution of the planets are proportional to the cubes of their mean distances from the Sun
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