Universal Gravitation, g, Escape Velocity and Satellites

Attempt the quiz above first, then review every question with its correct answer and a short explanation below.

1. Q1.The law of universal gravitation was given by:

   • A.Galileo Galilei
   • B.Johannes Kepler
   • C.Isaac Newton✓ Correct Answer
   • D.Albert Einstein

   Explanation: Newton published it in the Principia in 1687.

2. Q2.The value of g on the Earth's surface is about:

   • A.6.67 m/s²
   • B.1.6 m/s²
   • C.9.8 m/s²✓ Correct Answer
   • D.11.2 m/s²

   Explanation: g is the acceleration due to Earth's gravity.

3. Q3.The SI unit of the gravitational constant G is:

   • A.N kg^-1
   • B.N m² kg^-2✓ Correct Answer
   • C.N m
   • D.m s^-2

   Explanation: From F = G m1 m2 / r².

4. Q4.Astronauts inside an orbiting satellite experience:

   • A.double weight
   • B.zero mass
   • C.no gravity at all
   • D.weightlessness✓ Correct Answer

   Explanation: They are in continuous free fall around the Earth.

5. Q5.The mass of a body on the Moon compared with its mass on Earth is:

   • A.one-sixth
   • B.six times
   • C.zero
   • D.the same✓ Correct Answer

   Explanation: Mass is constant; only weight changes.

6. Q6.The value of g on the Moon compared with Earth is about:

   • A.one-half
   • B.one-sixth✓ Correct Answer
   • C.double
   • D.equal

   Explanation: The Moon has less mass and a smaller radius.

7. Q7.The value of the gravitational constant G is approximately:

   • A.6.67 × 10^-11 N m² kg^-2✓ Correct Answer
   • B.9.8 N m² kg^-2
   • C.6.67 × 10^11 N m² kg^-2
   • D.3 × 10^8 N m² kg^-2

   Explanation: It was first measured by Cavendish.

8. Q8.The escape velocity from the Earth is approximately:

   • A.11.2 km/s✓ Correct Answer
   • B.7.9 km/s
   • C.3 km/s
   • D.25 km/s

   Explanation: Beyond this speed an object leaves Earth's gravity.

9. Q9.The orbital velocity of a satellite close to the Earth is approximately:

   • A.11.2 km/s
   • B.7.9 km/s✓ Correct Answer
   • C.3 km/s
   • D.30 km/s

   Explanation: Escape velocity is √2 times orbital velocity.

10. Q10.The value of g is greater at the:

    • A.equator than at the poles
    • B.same everywhere
    • C.poles than at the equator✓ Correct Answer
    • D.centre of the Earth

    Explanation: The Earth bulges at the equator and rotates, reducing g there.

11. Q11.The value of g at the centre of the Earth is:

    • A.maximum
    • B.9.8 m/s²
    • C.infinite
    • D.zero✓ Correct Answer

    Explanation: Attractions from all sides cancel.

12. Q12.Kepler's second law states that a planet sweeps:

    • A.equal areas in equal intervals of time✓ Correct Answer
    • B.equal distances in equal times
    • C.a circle only
    • D.areas proportional to its mass

    Explanation: This implies faster motion near the Sun.

13. Q13.The time period of a geostationary satellite is:

    • A.12 hours
    • B.90 minutes
    • C.24 hours✓ Correct Answer
    • D.1 week

    Explanation: It matches the Earth's rotation period.

14. Q14.As we go higher above the Earth's surface, the value of g:

    • A.increases
    • B.stays constant
    • C.becomes infinite
    • D.decreases✓ Correct Answer

    Explanation: g falls with the square of distance from the centre.

15. Q15.If the distance between two masses is doubled, the gravitational force becomes:

    • A.one-fourth✓ Correct Answer
    • B.half
    • C.double
    • D.four times

    Explanation: Force is inversely proportional to the square of distance.

16. Q16.The escape velocity of a body does not depend on:

    • A.the mass of the body✓ Correct Answer
    • B.the mass of the planet
    • C.the radius of the planet
    • D.the value of G

    Explanation: v = √(2GM/R) contains no term for the object's mass.

17. Q17.The height of a geostationary satellite above the Earth's surface is about:

    • A.400 km
    • B.36,000 km✓ Correct Answer
    • C.3,600 km
    • D.3,60,000 km

    Explanation: It orbits above the equator at this height.

18. Q18.Kepler's third law states that the square of the time period is proportional to the:

    • A.square of the orbital radius
    • B.cube of the semi-major axis of the orbit✓ Correct Answer
    • C.orbital radius
    • D.mass of the planet

    Explanation: T² ∝ a³.

19. Q19.A person of mass 60 kg on the Moon has a weight equal to that of about what mass on Earth?

    • A.60 kg
    • B.360 kg
    • C.10 kg✓ Correct Answer
    • D.30 kg

    Explanation: Lunar gravity is about one-sixth: 60/6 = 10.

20. Q20.The time period of a satellite orbiting very close to the Earth is about:

    • A.24 hours
    • B.12 hours
    • C.10 minutes
    • D.84 minutes✓ Correct Answer

    Explanation: T = 2π√(R/g) is about 84 minutes.