# Gravitation - Chapter No 12

Right Answers have been shown below in red color.

1. In the formula F = Gm1m2/r2, the quantity G:

A. depends on the local value of g
B. is used only when Earth is one of the two masses
C. is greatest at the surface of Earth
D. is a universal constant of nature
E. is related to the Sun in the same way that g is related to Earth

2. The magnitude of the acceleration of a planet in orbit around the Sun is proportional to:

A. the mass of the planet
B. the mass of the Sun
C. the distance between the planet and the Sun
D. the reciprocal of the distance between the planet and the Sun
E. the product of the mass of the planet and the mass of the Sun

3. Suitable units for the gravitational constant G are:

. kg·m/s2
B. m/s2
C. N·s/m
D. kg·m/s
E. m3/(kg·s2)

4. The gravitational constant G has the derived units:

A. N·m
B. N·m/kg
C. N·kg/m
D. N·m2/kg2
E. N·kg2/m2

5. Earth exerts a gravitational force on the Moon, keeping it in its orbit. The reaction to this force, in the sense of Newton’s third law, is:

A. the centripetal force on the Moon
B. the nearly circular orbit of the Moon
C. the gravitational force on Earth by the Moon
D. the tides due to theMoon
E. the apple hitting Newton on the head.

6. A particle might be placed
1. inside a uniform spherical shell of mass M, but not at the center
2. inside a uniform spherical shell of mass M, at the center
3. outside a uniform spherical shell of mass M, a distance r from the center
4. outside a uniform solid sphere of mass M, a distance 2r from the center
Rank these situations according to the magnitude of the gravitational force on the particle, least to greatest.

A. All tie
B. 1, 2, 3, 4
C. 1 and 2 tie, then 3 and 4 tie
D. 1 and 2 tie, then 3, then 4
E. 1 and 2 tie, then 4, then 3

7. Three particles, two with mass m and one with mass M, might be arranged in any of the four configurations known below. Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.

A. 1, 2, 3, 4
B. 2, 1, 3, 4
C. 2, 1, 4, 3
D. 2, 3, 4, 2
E. 2, 3, 2, 4

8. Four particles, each with mass m are arranged symmetrically about the origin on the x axis. A fifth particle, with mass M, is on the y axis. The direction of the gravitational force on M
is:

A. ↑
B. ↓
C. ←
D. →
E. none of these directions

9. Let F1 be the magnitude of the gravitational force exerted on the Sun by Earth and F2 be the magnitude of the force exerted on Earth by the Sun. Then:
A. F1 is much greater than F2 B. F1 is slightly greater than F2 C. F1 is equal to F2 D. F1 is slightly less than F2 E. F1 is much less than F2

10. Let M denote the mass of Earth and let R denote its radius. The ratio g/G at Earth’s surface is:

A. R2/M
B. M/R2
C. MR2
D. M/R
E. R/M

11. Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times the diameter of Earth. The acceleration of a body falling near the surface of Venus is about:

A. 0.21 m/s2
B. 1.4 m/s2
C. 2.8 m/s2
D. 3.8 m/s2
E. 25 m/s2

12. The approximate value of g at an altitude above Earth equal to one Earth diameter is:

A. 9.8 m/s2
B. 4.9 m/s2
C. 2.5 m/s2
D. 1.9 m/s2
E. 1.1 m/s2

13. A rocket ship is coasting toward a planet. Its captain wishes to know the value of g at the surface of the planet. This may be inferred by:

A. measuring the apparent weight of one of the crew
B. measuring the apparent weight of an object of known mass in the ship
C. measuring the diameter of the planet
D. measuring the density of the planet
E. observing the ship’s acceleration and correcting for the distance from the center of the planet.

14. To measure the mass of a planet with the same radius as Earth, an astronaut drops an object from rest (relative to the planet) from an altitude of one radius above the surface. When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth. In units of Earth masses, the mass of the planet is:

A. 2
B. 4
C. 8
D. 16
E. 32

15. Suppose you have a pendulum clock that keeps correct time on Earth (acceleration due to gravity = 9.8 m/s2). Without changing the clock, you take it to the Moon (acceleration due to gravity = 1.6 m/s2). For every hour interval (on Earth) the Moon clock will record:

A. (9.8/1.6) h
B. 1 h
C. √(9.8/1.6) h
D. (1.6/9.8) h
E. √(1.6/9.8) h

16. The mass of an object:

A. is slightly different at different locations on Earth
B. is a vector
C. is independent of the acceleration due to gravity
D. is the same for all objects of the same size and shape
E. can be measured directly and accurately on a spring scale

17. An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they land together shows that:

A. no gravity forces act on a body in a vacuum
B. the acceleration due to gravity on the Moon is less than on Earth
C. in the absence of air resistance all bodies at a given location fall with the same acceleration
D. the feather has a greater weight on the Moon than on Earth
E. G = 0 on the Moon

18. The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet?

A. 24 N
B. 48 N
C. 96 N
D. 192 N
E. 600 N

19. An object at the surface of Earth (at a distance R from the center of Earth) weighs 90 N. Its weight at a distance 3R from the center of Earth is:

A. 10 N
B. 30 N
C. 90 N
D. 270 N
E. 810 N

20. An object is raised from the surface of Earth to a height of two Earth radii above Earth. Then:

A. its mass increases and its weight remains constant
B. both its mass and weight remain constant
C. its mass remains constant and its weight decreases
D. both its mass and its weight decrease
E. its mass remains constant and its weight increases