Question

1.   In applying the gravity method, we subtract the scalar magnitude of normal gravity (g_N) from the magnitude of the total component of the gravitational field (g_T) to estimate the magnitude of gravity acceleration in the vertical to the ellipsoid (g_z). Expand the error of this assumption using the binomial theorem to show that it is maximum at (g_A²/g_N), where (g_A) is the magnitude of the gravity effect of the anomalous mass.

2. (a) What is the difference between weight and mass?

      (b) When are they equivalent?

      (c) What are their respective units in the SIu system?

3.   Gravity force is always positive; however, in geophysical exploration many gravity anomalies are negative such as those associated with salt diapers in the Gulf Coast of the US. Explain.

4.   A gravity anomaly is determined to be 10 mGal. What is its value in

      (a) cm/s²,

      (b) m/s²,

      (c) μGal, and

      (d) the gravity unit?

5.   (a) Is the geoid a surface of equal gravitational acceleration? Explain.

(b) The International Gravity Formula gives the gravity of the Earth on what surface?

6.   How does the gravity on the surface of the Moon compare with that on the Earth considering that the Moon’s radius and mass, respectively, are roughly one-quarter and one-eightieth of those of the Earth.

7. The potential of g is G = (x² + y²)⁻¹.

      (a) Find g.

      (b) Describe the field lines, and

      (c) equipotential surfaces of g.

      (d) Demonstrate by integrating around the perimeter of a rectangle in the (x, y)-plane that g is conservative.

Answer 1

2a)

Mass:

• Mass is the amount of matter contained in a body.
• Mass of the body is the constant quantity and does not change with the change of position or location.

Weight:

• Weight is the force by which the earth attracts a body toward its centre, Or we can say it is the force on the object which is offered by the gravity
• Weight of the body is the variable quantity and changes with the change in position and location due to the acceleration of the gravity acting on it. Yes they are used at different places and time.

So these are the basic difference between Weight and Mass of the object

2b)

Mass and weight are NEVER the same, because mass is a measure of the amount of MATERIAL making a body (or a "thing") what it is, and weight is a measure of the FORCE that gravity provides on the body

weight = m*g

2c)

the SI units of mass is kg

the SI units of weight is Newtons (N)

4.solution

In SI base units, 1 Gal is equal to 0.01 m/s².

a) 10 m Gal = 0.01 cm / s²

b) 10 m Gal = 0.0001 m/s²

c) 10 m Gal = 10000 μ Gal

d) the SI unit of gravity is m/s²

6.solution

g = acceleration due to gravity (units m/s2)

G = the universal gravitational constant, G = 6.673 x 10-11N·m2kg2

m = mass of a moon = 1/8 mass of earth

m = 5.972*10²⁴ / 8 = 7.46*10²³ kg

r = radius of moon = 1/4 radius of earth

r = 6371*10³ / 4 = 1.59*10⁶ m

Acceleration Due to Gravity Formula Questions:

g = Gm / r² = 6.66*10^-11*7.46*10²³ kg / (1.59*10⁶)²

g = 19.69 m/s²