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Q71. The coefficients of permeability of two aquifers – 1 and 2, are 60 m/day and 40 m/day, respectively. Their saturated thicknesses are 30 m and 15 m, respectively. Assuming steady state Darcian flow, the transmissivity of aquifer 1 is ________ times that of aquifer 2. (In integer)
The correct answer is 3. 'Transmissivity' measures how easily water can completely blast through a whole wall of underground rock. You calculate it simply by multiplying how easy the rock is to flow through (permeability) by the height of the water wall (thickness). For Aquifer 1, 60 multiplied by 30 is 1800. For Aquifer 2, 40 multiplied by 15 is 600. To find out how much more powerful Aquifer 1 is, divide 1800 by 600. The result is exactly 3 times more transmissive.
Q72. The cut-off grade of copper is 0.45 wt%. A mine has 1 million tonne of waste with a grade of 0.25 wt%. The mine also has stock of high grade ore with a grade of 1.8 wt%. How much of this high grade ore (in million tonne) must be blended with the waste to sell the blended ore at a grade of 0.5 wt%? (Round off to three decimal places)
The correct answer is 0.192. This is a mixing math problem. You have 1 part poor dirt (0.25% copper) and want to mix an unknown amount (X) of rich dirt (1.8% copper) until the whole pile averages out to exactly 0.5% copper. The formula equates the copper in both separate piles to the copper in the final mixed pile: (1 * 0.25) + (X * 1.8) = 0.5 * (1 + X). Solving this algebra reveals that 1.3 times X equals 0.25. Dividing 0.25 by 1.3 shows you need about 0.192 million tonnes of rich ore.
Q73. The mass of the Earth is 80 times that of the Moon while the radius of the Earth is four times that of the Moon. The surface gravity of the Earth is ______ times that of the Moon? (In integer)
The correct answer is 5. Isaac Newton's law of gravity states that gravity depends on how heavy a planet is (mass) divided by its size squared (radius squared). The Earth's mass makes gravity 80 times stronger. However, because Earth is 4 times wider, we square that 4 to get 16. Being bigger pushes the surface further from the center, which weakens gravity by a factor of 16. Finally, take the mass boost (80) and divide it by the size penalty (16). 80 ÷ 16 equals exactly 5 times the gravity.
Q74. The maximum and minimum principal stresses in a zone of active normal faulting are 28 MPa and 8 MPa, respectively. The fault plane strikes N30ºE and dips 60º towards SE. Considering Anderson’s theory of faulting, the normal stress on the fault plane is ____________ MPa. (In integer)
The correct answer is 13. To find how much pressure is pushing straight down onto a slanted fault crack, geologists use stress circle math. Because the fault dips at 60 degrees, the angle it makes with the crushing vertical pressure is 60 degrees. The formula for normal pressure is the average of the two stresses PLUS half their difference multiplied by the cosine of double the angle. The average is 18. Half the difference is 10. Double the angle is 120. The cosine of 120 is -0.5. So, 18 plus (10 * -0.5) equals 18 minus 5, which perfectly equals 13 MPa.
Q75. The radius of the Earth’s circular orbit round the Sun is 149×106 km. The Earth takes 365 days to orbit the Sun. The tangential velocity of the Earth is ____________ km/hour. ( = 3.14) (Round off to one decimal place)
The correct answer is 106817. To find how fast Earth flies through space, we must calculate the total distance it travels and divide by the time it takes. The circular orbit path is the circumference (2 × 3.14 × 149,000,000 km), which equals 935,720,000 kilometers traveled in one year. To find speed per hour, multiply 365 days by 24 hours to get 8,760 total hours. Finally, divide the distance (935,720,000) by the hours (8,760) to get a speed of approximately 106,817 kilometers per hour.
Q76. Using Airy’s hypothesis, calculate the thickness of the root beneath a 4 km high mountain in isostatic equilibrium with a 40 km thick continental crust of density 2800 kg/m3 and a mantle of density 3300 kg/m3. Express your answer in km. (Round off to one decimal place)
The correct answer is 22.4. Mountains act exactly like icebergs; to float 4 kilometers high in the air, they must have a massive, deep 'root' pushing down into the heavy mantle below. Airy's geology formula dictates that the Root thickness = (Mountain Height × Crust Density) ÷ (Mantle Density - Crust Density). Plugging the numbers in: (4 × 2800) ÷ (3300 - 2800). This simplifies to 11200 divided by the density difference of 500. Doing the math gives exactly 22.4 kilometers of deep root holding up that mountain.
Q77. Within a fourth order drainage basin, the total lengths of the 1st, 2nd, 3rd and 4th order streams are 10.5 km, 7.5 km, 5.5 km and 1.5 km, respectively. If the drainage density of the basin is 0.5 km-1, the basin area is _________ km2. (In integer)
The correct answer is 50. 'Drainage density' is a measure of how crowded a map is with rivers. The mathematical formula is simple: Drainage Density = Total Length of all streams ÷ Total Area of the basin. First, add up the lengths of every stream (10.5 + 7.5 + 5.5 + 1.5) to get a total of 25 km of rivers. To find the area, divide the total length (25) by the given density (0.5). 25 ÷ 0.5 equals exactly 50 square kilometers.
Q78. In a structurally controlled fluvial setting, an asymmetric flight of river terraces T1, T2, T3 shown in the figure was sampled at location L1. The age of the sample at L1 was 30 ka (kiloyears). Assuming that the terraces were formed entirely due to deformation related uplift, the average uplift rate in the past 30 ka in the region was _______________ mm/yr. (Answer in integer).
The correct answer is 10. The highest terrace (L1) was once at the exact same level as the river, but tectonic forces have shoved the land upwards. L1 is currently sitting at an elevation of 400 meters, while the present-day river is down at 100 meters. The total vertical uplift is 300 meters, which equals 300,000 millimeters. This entire lift happened over 30,000 years (30 ka). Dividing the distance (300,000 mm) by the time (30,000 yrs) gives a perfectly steady geological uplift rate of exactly 10 mm/yr.
Q79. In the uvavorite garnet (Ca3+2Cr2+3Si3+4O12), Ca is in cubic coordination, Cr is in octahedral coordination and Si is in tetrahedral coordination. The electrostatic bond strength of the Ca2+ central ion is _______. (Round off to two decimal places).
The correct answer is 0.25. In crystal chemistry, Pauling's rule dictates that the 'electrostatic bond strength' reaching out from a central metal atom is simply calculated by taking its electrical charge and dividing it equally among the total number of oxygen atoms surrounding it. The Calcium (Ca) ion has a charge of +2. Because it sits in a 'cubic coordination', it is physically surrounded by exactly 8 oxygen atoms. Dividing the charge (2) by the coordination number (8) equals exactly 0.25.
Q80. A crystal has lattice parameters of a : 4.26 Å, b : 10 Å and c : 3.44 Å, respectively. A plane intercepts on the a, b and c axes at 2.13 Å, 10 Å and 1.72 Å, respectively. The Miller Indices for the plane, written as an integer, is _____________
The correct answer is 212. Geologists use 'Miller Indices' to cleanly describe how a plane cuts through a crystal lattice. First, divide the physical intercepts by the lattice parameters to find the unit intercepts: (2.13/4.26) = 1/2 for a, (10/10) = 1 for b, and (1.72/3.44) = 1/2 for c. Next, strictly take the mathematical reciprocals (flip them upside down) to get the final indices: 2, 1, and 2. Written as a single integer, this is perfectly represented as 212.