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Q61. A borehole inclined at 60º to the horizontal pierces a vertical basaltic dyke of uniform thickness. If the length of the basaltic drill core along the core axis is 12 m, the thickness of the dyke is ____________ m. (In integer)
The correct answer is 6. Imagine a perfectly straight, upright wall of rock (a vertical dyke). A drill is angled diagonally downwards at 60 degrees from the flat ground. Because it cuts diagonally through the upright wall, it travels a long path (12 meters) to get through. The true, shortest thickness of the wall is found using trigonometry: multiply the diagonal drilled length (12) by the cosine of the drill angle (60 degrees). Since the cosine of 60 is exactly 0.5, multiplying 12 by 0.5 gives a true thickness of 6 meters.
Q62. A cylindrical soil sample is encased in an open-ended inclined tube with a diameter of 100 mm. There is a constant supply of water from the upper end of the sample and the outflow from the other end is collected in a beaker. The average amount of water collected is 1000 mm3 every 10 sec. The average outflow velocity is__________ mm/sec. ( = 3.14) (Round off to three decimal places)
The correct answer is 0.013. Velocity of water escaping a pipe is the volume of water divided by the time it took, and then divided by the flat area of the pipe. First, 1000 cubic millimeters dripping every 10 seconds means the flow rate is 100 mm3 per second. Second, calculate the area of the 100 mm wide circle: radius (50) squared times 3.14 equals 7850 square millimeters. Lastly, dividing the flow rate (100) by the area (7850) gives an incredibly slow velocity of roughly 0.0127 millimeters per second, rounding to 0.013.
Q63. A granite block starts sliding on a slope (inclination of 30º with the horizontal) under the effect of gravity only, along the true direction of inclination of the slope and hits the ground in 4 seconds. Considering zero friction and zero cohesion during sliding, the vertical height of the point (with respect to the ground) from where the block was dislodged is ____________ m. (g = 10 m/s2) (In integer)
The correct answer is 20. First, figure out how fast gravity pulled the rock down the slant. Because the slope is 30 degrees, gravity's acceleration down the ramp is halved (10 * sine of 30 degrees = 5 meters/second squared). Next, calculate the total distance it slid in 4 seconds using the falling object formula (0.5 * acceleration * time squared). 0.5 * 5 * 16 seconds gives a total slide distance of 40 meters. Finally, since the slide was 40 meters long on a 30-degree ramp, the actual vertical drop is 40 * sine(30), which equals exactly 20 meters high.
Q64. A hypothetical rock contains the assemblage kyanite, sillimanite and quartz. The variance (degree of freedom) of the assemblage is _________. (In integer)
The correct answer is 1. Geologists use a chemistry rule called the 'Phase Rule' to figure out how many things (like temperature or pressure) can be changed without destroying the minerals in a rock. The formula is: Degrees of Freedom = Components - Phases + 2. Kyanite and Sillimanite are the exact same chemical (Al2SiO5), just in different shapes, and Quartz is SiO2. So, there are 2 basic components. We physically see 3 mineral phases. The math is 2 minus 3 plus 2, which equals 1 degree of freedom.
Q65. A P-ray arrives at the mantle-core boundary at an angle 25o with respect to the normal. At what angle to the normal does it enter the core? (P-wave velocity in the lower mantle is 13.7 km/s and outer core is 8.1 km/s) (Round off to two decimal places)
The correct answer is 14.47. When an earthquake wave hits a boundary where rock density changes, it bends (refracts). Physics uses 'Snell's Law' to predict this bending: sine(angle 1) ÷ Velocity 1 = sine(angle 2) ÷ Velocity 2. The sine of the incoming 25-degree angle is roughly 0.4226. Dividing this by the mantle speed (13.7) gives 0.0308. Multiplying this by the core speed (8.1) gives the sine of the new angle as 0.2498. Using a calculator to find the inverse sine of 0.2498 reveals the wave bent to an angle of 14.47 degrees.
Q66. A soil has a void ratio of 0.5. The total porosity of the soil is __________. (Round off to two decimal places)
The correct answer is 0.33. 'Void ratio' compares the amount of empty space in dirt to the solid dirt grains. 'Porosity' compares that same empty space to the ENTIRE chunk of dirt overall. You can convert them using this engineering formula: Porosity = Void Ratio ÷ (1 + Void Ratio). So, take 0.5 and divide it by 1.5. The math gives 0.3333..., which rounds to 0.33. This means 33% of the soil chunk is empty space.
Q67. Assume that 218Po, with a half-life of 138 days, is in secular equilibrium with 238U whose half-life is 4.5 × 109 y. How many grams of 218Po will be present for each gram of 238U in the mineral? Express your answer in logarithm (to the base 10). (Round off to two decimal places)
The correct answer is -10.08. 'Secular equilibrium' is a radioactive traffic jam where a fast-decaying element (Polonium) gets trapped waiting in line behind an incredibly slow-decaying parent (Uranium). Because Uranium is billions of times slower, practically the entire physical mass of the rock remains Uranium, with only an invisible, microscopic fraction of Polonium existing at any one second. By taking the ratio of their half-lives (138 days divided by 4.5 billion years in days) and correcting for their slightly different atomic weights, we find the tiny fraction is about 7.69 × 10^-11 grams. The base-10 logarithm of that incredibly tiny fraction is -10.08.
Q68. Given atomic weights of Cu, Fe and S as 63.55, 55.85 and 32.10, respectively, find out the weight of copper (in gram) metal in an ore (no associated gangue) of 1 kg weight constituting of bornite, chalcopyrite and chalcocite present in weight fractions of 0.4, 0.4 and 0.2, respectively. (Round off to one decimal place)
The correct answer is 551.8. You have 1000 grams total of rock. This means you have 400g of Bornite, 400g of Chalcopyrite, and 200g of Chalcocite. First, use the atomic weights to find what percentage of each mineral's chemistry is pure copper. Bornite (Cu5FeS4) is mathematically about 63.3% copper. Chalcopyrite (CuFeS2) is about 34.6% copper. Chalcocite (Cu2S) is about 79.8% copper. Multiply these percentages by the physical weight of each mineral: (0.633 × 400g) + (0.346 × 400g) + (0.798 × 200g). Adding all the pure copper pieces together gives roughly 551.8 grams total.
Q69. The 87Sr/86Sr ratio of a 1000 Ma granite was measured as 0.8001. If its 87Rb/86Sr ratio is 2.499, what was the Sr isotopic ratio of the source at the time of derivation of the granite? (decay constant of 87Rb=1.39 × 10-11 yr-1) (Round off to three places of decimals)
The correct answer is 0.765. Radioactive Rubidium acts like a clock, slowly decaying into Strontium over time. To find out what the rock's chemistry looked like 1 billion years ago (1000 Ma), we have to mathematically 'rewind' the clock and subtract the newly created Strontium from the current total (0.8001). Using the decay equation, the amount generated is the Rubidium amount (2.499) multiplied by the decay over 1 billion years (roughly 0.014). This generated portion is about 0.035. Subtracting 0.035 from today's 0.8001 reveals the starting chemistry was 0.765.
Q70. The average unit weight of the uppermost part of the crust is 25000 N/m3. The vertical stress at a depth of 1 km would be ___________ MPa. (In integer)
The correct answer is 25. 'Vertical stress' is just the crushing weight of all the rock stacked above a point. To find it, you multiply the heavy weight of the rock per meter by how deep you dig. The depth is 1 kilometer, which is 1,000 meters. 25,000 N/m3 multiplied by 1,000 meters is 25,000,000 Pascals of pressure. Since 1 Megapascal (MPa) is exactly one million Pascals, you simply divide by one million to get exactly 25 MPa.