Question

Please make sure to answer all the questions correctly;

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

a)

weight:1. force acting on object due to gravity. it is a vector quantity and directed perpendicula downward towards the gravity

Mass:- total material pressent in an object. it is a scalar quantity.

b) in weightless ness i.e in freefall mass is equivalent to weight

c) weight unit = Newton(N)

mass unit= kilogram(mg)

3)

lesser denser rock such as sedimentary basin,batholits,oceanic ridges produces negative amomalies. rapid change in amplitude nad gradiant results in density chsnge. this decrease of density results in negative gravity force.

4)a) 1 m gal=10^-3cm/sec²

10mGal=10*10^-3 cm/sec²=0.01cm/sec²

^b)

1 mGal= 10^-5m/sec²

10mGal=10*10^-5m/sec²=10^-4m/sec²

^c) 1 mGal=10^{-3 microgal}

10 mGal=10*10³ microgal=10⁴microgal

d) 1 mGal=1.02*10^-6g

10 mGal=1.02*10^-5g