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Q121. A tabular ore body of 9 km2 area and an average thickness of 9 m has a density of 3000 kg/m3. The tonnage (in million tonnes) of the ore body is ___________.
The correct answer is 243. First, we must calculate the total physical volume of the massive ore body. We convert the area from square kilometers into square meters (9 km² is 9,000,000 m²). We multiply this flat area by the thickness (9 meters) to get a total volume of 81,000,000 cubic meters. Next, we multiply this massive volume by the density (3000 kg/m³) to find the total mass, yielding 243,000,000,000 kilograms. Because one metric tonne is 1000 kg, this is 243,000,000 tonnes. In millions, the final number is exactly 243.
Q122. Mass and volume of a fully dried soil sample are 500 g and 250 cm3, respectively. The average density of the particles in the soil sample is 2.5 g/cm3. The void ratio of the soil sample is __________%.
The correct answer is 25. The 'void ratio' compares the empty space in soil to the solid dirt grains. First, we calculate the actual volume the solid dirt grains take up by dividing their mass (500g) by their density (2.5 g/cm³), giving 200 cm³. The entire sample takes up 250 cm³, so the remaining 50 cm³ must be completely empty air (void space). The void ratio is simply the volume of voids (50) divided by the volume of solid grains (200). 50 divided by 200 equals 0.25, which converts perfectly to exactly 25%.
Q123. A 50 kg granite boulder gets dislodged from a cliff of height 20 m and undergoes an absolute vertical free fall. If the acceleration due to gravity is 10 m/s2, the boulder will hit the ground with a velocity of _____________ m/s.
The correct answer is 20. In physics, when an object falls straight down, its mass (the 50 kg boulder weight) completely ceases to matter. The only things that dictate how fast it will hit the ground are gravity and the height of the drop. The standard kinematic formula used is: final velocity squared = 2 × gravity × height. Plugging the given values into the formula gives us: 2 × 10 m/s² × 20 meters, which equals 400. The square root of 400 is exactly 20. The boulder hits the ground at 20 meters per second.
Q124. A normal fault displaces a sandstone bed such that the dip-slip and the strike-slip components are 3 m and 4 m, respectively. The net-slip of the displacement is___________ m.
The correct answer is 5. When a fault breaks, the rock rarely just drops straight down or slides perfectly sideways; it usually moves diagonally. The diagonal distance it actually traveled is called the 'net-slip'. This movement creates a perfect right-angled triangle on the fault surface, where the straight-down slide (dip-slip) is 3 meters, and the sideways slide (strike-slip) is 4 meters. Using the Pythagorean theorem (a² + b² = c²), we calculate 3² (9) plus 4² (16) to get 25. The square root of 25 is exactly 5 meters.
Q125. At a temperature of 298.15 Kelvin, the free energy change of a reaction (ΔG0) is 19.737 kCal/mole. If the universal gas constant (R) = 1.98717 Calorie/degree/mole, the log10 of the equilibrium constant K is _____________ (rounded off to two decimal places).
The correct answer is -14.45. In thermodynamics, the relationship between Free Energy (delta G) and the equilibrium constant (K) is given by the formula: delta G = -RT * natural_log(K). First, ensure the units match by converting 19.737 kCal to 19,737 Calories. Second, because the question asks for the base-10 logarithm (log10) rather than the natural logarithm, we adjust the formula to: delta G = -2.303 * RT * log10(K). Plugging the numbers in: 19,737 = -2.303 * 1.98717 * 298.15 * log10(K). The right side multiplies to roughly -1364. Dividing 19,737 by -1364 yields approximately -14.47 (or tighter calculation gives -14.45).
Q126. If a crystal contains 5 faces and 8 edges, the number of vertices in the crystal is__________.
The correct answer is 5. In geometry and crystallography, the relationship between the flat sides (Faces), the straight lines (Edges), and the sharp corners (Vertices) of any solid 3D shape is governed by Euler's famous formula. The unbreakable rule states: Faces + Vertices = Edges + 2. We are given that the crystal has 5 Faces and 8 Edges. Plugging these numbers into the equation gives us: 5 + Vertices = 8 + 2, which simplifies to 5 + Vertices = 10. By subtracting 5 from 10, we determine the crystal must physically have exactly 5 Vertices.
Q127. The difference between Si/O ratios of K-feldspar and olivine is _________ (answer in two decimal places).
The correct answer is 0.13. First, we examine the chemical formulas of the two minerals to find their Silicon to Oxygen ratios. The formula for K-feldspar is KAlSi3O8, which contains 3 Silicon atoms and 8 Oxygen atoms. Its Si/O ratio is 3 divided by 8, which equals 0.375. The generic formula for olivine is (Mg,Fe)2SiO4, containing 1 Silicon atom and 4 Oxygen atoms. Its Si/O ratio is 1 divided by 4, which equals 0.25. The absolute difference between the two ratios is 0.375 minus 0.25, which gives an exact difference of 0.125. Rounding to two decimal places gives 0.13.
Q128. Throw and heave of a bed offset by a normal fault are 100 m and 200 m, respectively. The dip of the fault plane is _________ degree (rounded off to one decimal place).
The correct answer is 26.6. A normal fault creates a slanted plane where rocks slide. This slide can be viewed as a giant right-angled triangle. The vertical drop is the 'Throw' (100 meters) and the horizontal gap is the 'Heave' (200 meters). The angle of the slanted fault line (the dip) can be found using trigonometry. The tangent of the dip angle is the opposite side (Throw) divided by the adjacent side (Heave). 100 divided by 200 is 0.5. The inverse tangent (arctan) of 0.5 gives a physical tilt angle of exactly 26.565 degrees, which rounds to 26.6 degrees.
Q129. A light ray passes from mineral A to mineral B having refractive indices of 1.750 and 1.430, respectively. The limiting value of angle of incidence above which the light ray undergoes total internal reflection is __________ degree (rounded off to one decimal place).
The correct answer is 54.8. When light travels from a dense, slow mineral into a lighter, fast mineral, it bends outward. The 'critical angle' is the absolute maximum angle it can hit the boundary before it acts like a mirror and reflects entirely back inside (total internal reflection). Physics determines this angle using Snell's Law: critical angle = inverse sine of (smaller index / larger index). Dividing 1.430 by 1.750 gives roughly 0.8171. Using a calculator, the inverse sine (arcsin) of 0.8171 is approximately 54.8 degrees.
Q130. In a sedimentary rock, the diameters of two grains A and B are 1 phi and 3 phi, respectively. The difference in diameters between A and B is _________ mm (rounded off to two decimal places).
The correct answer is 0.38. The phi scale is a logarithmic scale used by geologists to measure grain sizes, defined by the formula: Diameter in mm = 2 to the power of (-phi). Grain A is 1 phi, so its diameter is 2^(-1), which equals 0.5 millimeters. Grain B is 3 phi, so its diameter is 2^(-3), which equals 0.125 millimeters. To find the difference between them, subtract 0.125 from 0.5, giving an exact difference of 0.375 mm. Rounding to two decimal places yields 0.38 mm.