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Q51. A one-meter deep and sheet-like waterflow on a sandy beach developed antidunes. The minimum velocity of the waterflow was ______________ m/s. (Round off to two decimal places) (Use g = 10 m/s2)
The correct answer is 3.10 to 3.20. Antidunes are special sand ripples that only form when water is flowing extremely fast—specifically, when the 'Froude number' hits 1 or more. The formula for the Froude number is Velocity ÷ square root of (gravity × depth). Setting the Froude number to 1, gravity to 10, and depth to 1, the math shows the water must be flowing at least the square root of 10, which is roughly 3.16 meters per second.
Q52. If the intercepts of crystallographic axes are 0.5a : 1b : 0.75c on a crystallographic plane {h k l}, the value of ‘l’ is _________. (In integer)
The correct answer is 4. Geologists use 'Miller Indices' (h, k, l) to define crystal faces. You find them by taking the intercepts, taking their reciprocals, and converting them to the smallest whole numbers. The intercepts are 1/2, 1, and 3/4. Flipping them upside down gives 2, 1, and 4/3. To remove the fraction, multiply all of them by 3. This gives the final indices as 6, 3, and 4. The 'l' value is the final number, which is 4.
Q53. The density of a FCC unit cell is 6.5 g/cm3. If the mass of a single atom is 60 g/mol, the diagonal length of the face {100} is ______________ Å. (Round off to two decimal places) (Use NA = 6.022 × 1023)
The correct answer is 5.55 to 5.59. A Face-Centered Cubic (FCC) crystal unit contains exactly 4 atoms. By using the mass given and Avogadro's number, we find the weight of those 4 atoms. Dividing this weight by the density (6.5) gives us the physical volume of the microscopic cube. Taking the cube root gives the edge length of the cube (about 3.94 Ångströms). The diagonal across the square face is calculated using the Pythagorean theorem, resulting in roughly 5.57 Ångströms
Q54. The amplitude recorded at a station for a magnitude 5 earthquake is 𝑥. If another earthquake recorded at the same station has an amplitude of 15𝑥, then the magnitude of this earthquake is _______. (Round off to two decimal places)
The correct answer is 6.15 to 6.19. The earthquake magnitude scale is logarithmic. The formula linking magnitude (M) and amplitude (A) is M = log10(A) + constant. For the first quake, 5 = log10(x) + c. For the second, M2 = log10(15x) + c. Subtracting the two gives M2 - 5 = log10(15). The log10 of 15 is roughly 1.176. Adding this to the original magnitude of 5 gives a new magnitude of roughly 6.18
Q55. The hydraulic conductivity of a 100 cm long cylindrical core is estimated as 1.2 cm/min when hydraulic head difference is 20 cm in an experimental setup. If the effective porosity of the core is 20%, then, assuming steady state Darcy flow, the average interstitial velocity of groundwater through the core is __________ m/day. (Round off to two decimal places)
The correct answer is 17.20 to 17.40. First, calculate the basic flow speed using Darcy's Law: conductivity (1.2 cm/min) multiplied by the pressure gradient (20 cm drop over 100 cm length, which is 0.2). This gives 0.24 cm/min. However, because water only travels through the 20% of the rock that is empty pore space, it must squeeze through much faster. Dividing 0.24 by the porosity (0.20) gives an actual water speed of 1.2 cm/min. Converting this into meters per day gives approximately 17.28 m/day.
Q56. An ocean wave with a wavelength of 200 m approaches the coast. If water depth at the observation point is 75 m, the wave velocity is ___________ m/s. (Round off to two decimal places) (Use g = 10 m/s2)
The correct answer is 17.50 to 18.00. Deep water waves have a speed determined purely by their wavelength. The formula is Speed = square root of (gravity × wavelength ÷ 2π). Calculating this gives roughly 17.8 meters per second.
Q57. If an iron ore body contains 50% hematite (Fe2O3) and 50% magnetite (Fe3O4), then the grade of the iron ore body is ________%. (Round off to two decimal places) (Use atomic weight of Fe = 55.85 amu and O = 16 amu).
The correct answer is 70.50 to 71.50. To find the overall 'grade' (iron percentage), we must find how much pure iron is locked inside each mineral. Using atomic weights, pure hematite is mathematically about 69.94% pure iron, and pure magnetite is about 72.36% pure iron. Because the ore is a perfectly equal 50/50 mix of the two minerals, we simply take the average of those two percentages, which equals roughly 71.15% pure iron overall.
Q58. A bed with an attitude 045, 20SE is rotated 60 clockwise (looking down) about a vertical axis. The strike value (in the azimuthal convention following right hand rule) of the rotated bed is ________ degrees. (In integer)
The correct answer is 105. 'Strike' is the compass direction of a flat rock layer measured in degrees from 0 to 360. The original strike is 45 degrees. If you physically rotate the entire block of rock clockwise by 60 degrees around a vertical pole, you simply add that 60 to the original compass reading. 45 degrees plus 60 degrees puts the new strike pointing exactly at 105 degrees.
Q59. The water table over an area of 1 km2 was lowered by 4 m. If the porosity of rock is 30% and the specific retention is 10%, the change in the groundwater storage is __________ × 103 m3. (In integer)
The correct answer is 800. An aquifer acts like a sponge. When the water level dropped by 4 meters over 1 square kilometer (1 million square meters), it drained a total rock volume of 4 million cubic meters. However, only the 'yield' water actually drains; 30% is empty space, but 10% stays stuck to the rock (retention), meaning only 20% actually drains out. 20% of 4 million is 800,000 cubic meters. The question asks for the answer in thousands, so the number is just 800.9
Q60. A cylindrical copper ore body has a vertical thickness of 45 m and a diameter of 14 m with a density of 2.9 g/cm3. The reserve of the copper ore body is _________ tons. (In integer)
The correct answer is 20070 to 20100. First, calculate the volume of the underground cylinder of ore using the formula: Volume = π × radius² × height. The radius is half the diameter (7m). So, π × 49 × 45 gives a volume of roughly 6,927 cubic meters. Next, multiply the volume by the density (2.9 tons per cubic meter). 6,927 × 2.9 equals approximately 20,088 tons of copper ore.