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Q31. The thickness of a dipping coal bed measured along a vertical drill hole is 15 m. If the dip of the coal bed is 30⁰, the orthogonal thickness of the coal bed is _______ m. (Round off to the nearest integer)
If a coal seam is tilted underground, drilling straight down through it will cut it at an angle, making the bed seem artificially thicker than it really is. To find the 'true' or orthogonal thickness (measuring perfectly perpendicular to the slanted layer), we multiply the vertical drilled thickness (15m) by the cosine of the tilt angle (30 degrees). 15 multiplied by 0.866 equals about 13 meters.
Q32. The fraction of 𝑁𝑎11 24 atoms remaining after a decay interval of 5.0 hours will be _______. (Round off to three decimal places) (Use t1/2 = 15.0 hours)
Radioactive elements decay over time. The 'half-life' is the time it takes for exactly half of the atoms to disappear. Here, the half-life is 15 hours. We want to know how much is left after only 5 hours. We can use a decay formula: Amount Left = (1/2) to the power of (time elapsed divided by half-life). So, (1/2) to the power of (5/15) is (0.5) to the power of 0.333, which equals roughly 0.794 remaining.
Q33. The lithostatic pressure at a depth of 36.5 km in the continental crust having an average density of 2800 kg/m3, is _______GPa. (Round off to the nearest integer) (Use g = 9.8 m/s2)
'Lithostatic pressure' is the crushing weight of all the rock stacked above a certain depth. It is calculated by multiplying depth × density × gravity. Depth is 36,500 meters, density is 2800, and gravity is 9.8. Multiplying these together gives 1,001,560,000 Pascals. A Gigapascal (GPa) is one billion Pascals. So dividing by one billion gives roughly 1.001 GPa, which rounds to exactly 1.
Q34. Clinopyroxene crystallizing from a basaltic magma has Sm concentration of 24 ppm. If the clinopyroxene-melt partition coefficient for Sm is 1.2, the concentration of Sm in the basaltic magma will be _______ ppm. (In integer)
A 'partition coefficient' is a ratio that tells us how a chemical element splits between a solid crystal and liquid magma. A coefficient of 1.2 means the crystal holds 1.2 times more of the element (Samarium) than the liquid magma. If the crystal has 24 parts per million (ppm), we divide 24 by 1.2 to find that the surrounding magma liquid had 20 ppm.
Q35. The area of a triangular block of a massive orebody is 1500 m2. If the thickness of the orebody is 5 m, 6 m and 7 m at the three corners of the triangular block, and the ore density is 2.5 tons/m3, the estimated ore reserve of the block is _______ tons. (In integer)
To find the total amount of ore, we first need to figure out its volume. Since the thickness varies at each corner of the triangle (5, 6, and 7 meters), we find the average thickness by adding them together and dividing by 3, which equals 6 meters. We multiply the flat area (1500 square meters) by this average thickness (6 meters) to get a total volume of 9000 cubic meters. Finally, multiplying the volume (9000) by the density (2.5 tons per cubic meter) gives us 22,500 tons.
Q36. The geothermal gradient in the continental crust is 0.02 ⁰C/m. If the surface temperature is 25 ⁰C, the temperature at a depth of 18 km from the surface is ______ ⁰C. (In integer)
The Earth gets hotter the deeper you go. The gradient tells us the temperature rises 0.02 degrees for every single meter we dig down. A depth of 18 kilometers is 18,000 meters. The total heat added over that depth is 18,000 meters multiplied by 0.02, which is 360 degrees. Add this to the starting surface temperature of 25 degrees, and the total temperature is 385 degrees Celsius.
Q37. An aquifer has a cross-sectional area of 10 m2 and a hydraulic conductivity of 0.25 cm/s. The volume of water that will flow per second through the aquifer for a hydraulic gradient of 0.04 is _______ cm3. (Round off to three decimal places)
We can calculate water flow using a simple formula: Total Flow = Area × Conductivity × Gradient. First, we must convert the area of 10 square meters into square centimeters by multiplying by 10,000 to get 100,000 cm². Then, we multiply 100,000 cm² by the conductivity (0.25) and the gradient (0.04). This gives us a flow of exactly 1000 cubic centimeters per second.
Q38. The mean flow velocity of water in an open channel having an average depth of 0.2 m, and with Froude Number 4, is _______m/s. (Round off to one decimal place) (Use g = 9.8 ms-2)
In water flow, the 'Froude Number' relates speed to water depth to tell us if the flow is calm or rapid. The formula is: Froude Number = Velocity / square_root(gravity * depth). If we know the Froude Number is 4, gravity is 9.8, and depth is 0.2, we multiply 9.8 by 0.2 to get 1.96. The square root of 1.96 is 1.4. Finally, 4 multiplied by 1.4 gives a water speed of 5.6 meters per second.
Q39. Consider the univariant metamorphic reaction Albite = Jadeite + Quartz. The minimum number of chemical components required to describe the composition of all the phases is _______. (In integer)
To mathematically describe this chemical reaction, we need to know the minimum number of basic chemical 'building blocks' involved. Even though there are three minerals, they can all be completely made from just two basic molecular ingredients: Sodium oxide (Na2O) mixed with Alumina (Al2O3), and Silica (SiO2). Thus, we only need 2 components.
Q40. The atom percent of Fe in pyrrhotite of composition Fe0.77S is _______. (Round off to two decimal places)
A mineral formula shows the ratio of atoms. For every 1 atom of Sulfur (S), there are 0.77 atoms of Iron (Fe). To find the percentage of Iron out of all the atoms, you add the parts together to get a total of 1.77. Then, you divide the Iron part (0.77) by the total (1.77) and multiply by 100. This equals about 43.50%.