General Science and Engineering Basics

To convert from radians per second to RPM, multiply by 60 (to get radians per minute) and divide by 2pi (since one revolution is 2pi radians). RPM = (w × 60) / (2pi). Option A would give radians per hour, while options C and D are incomplete conversions.

The formula for arc length when angle is in radians is s = R × theta, where theta is the angle in radians. This is because the definition of radian measure comes from arc length divided by radius. Option A would give circumference multiplied by angle, while option B incorrectly squares the radius.

L10 life in bearing terminology means that 90% of a group of identical bearings operating under identical conditions will survive for a minimum of 1 million revolutions before the first evidence of fatigue develops. The 'L10' designation specifically refers to the rating life at which 10% of bearings are expected to fail - meaning 90% survive.

To convert kilogram-force (kgf) to Newtons, multiply by gravitational acceleration (9.81 m/s²). Therefore, 100 kgf equals 100 × 9.81 = 981 Newtons, as 1 kgf = 9.81 N.

For an object starting from rest with constant acceleration 'a', the distance traveled after time 't' is given by s = 0.5 × a × t². This is derived from the kinematic equation for uniformly accelerated motion.

'Oil of Vitriol' is the historical archaic name for sulphuric acid (H₂SO₄), given by medieval alchemists due to its oily appearance and vitriolic (corrosive) nature. Nitric acid, acetic acid, and citric acid are different acids with distinct properties.

To balance Al(OH)₃ + 3HCl → AlCl₃ + 3H₂O, we need 3 H₂O molecules. Balancing: Al(1), Cl(3), O(3 on each side), H(6 on each side). The coefficient 3 ensures hydrogen and oxygen atoms are balanced.

Mercury is the only metal that is liquid at standard temperature and pressure. Its symbol Hg comes from 'hydrargyrum' (Greek for 'water silver'). Helium is a noble gas, silver is a solid metal, and radium is a solid radioactive metal.

On the pH scale, values below 7 are acidic, 7 is neutral, and above 7 are basic/alkaline. A pH of 2.5 is strongly acidic, indicating a high concentration of H⁺ ions.

Hydrogen is the most abundant element in the universe, comprising about 75% of all normal matter by mass. It was formed during the Big Bang nucleosynthesis and remains the primary fuel for stars through nuclear fusion. Iron, carbon, and oxygen are much less abundant on a cosmic scale.

The 20-tooth gear is weaker in bending. With fewer teeth, each tooth is smaller and has less root thickness compared to the 40-tooth gear, assuming the same module and material. Smaller teeth are more susceptible to bending failure under load.

An equinox is the date when day and night are approximately equal in length worldwide. This occurs twice yearly - around March 20 (vernal/spring equinox) and September 22 (autumnal equinox). Solstices mark the longest and shortest days, not equal days.

Benjamin Franklin invented the lightning conductor (lightning rod) in 1752 through his famous kite experiment demonstrating lightning's electrical nature. This invention protects buildings by safely conducting lightning strikes to the ground. Franklin was a polymath scientist, not primarily known for physics like Einstein or Newton.

The Pleistocene epoch (2.58 million to 11,700 years ago) is when Homo sapiens evolved and spread across the globe. This epoch was marked by repeated glaciations (ice ages) and the emergence of modern humans. The Holocene began after the Pleistocene (10,000 years ago to present), Mesozoic was the age of dinosaurs, and Cambrian was much earlier (541-485 million years ago).

Ammonia (NH3) is widely used as a fertilizer because it contains nitrogen, an essential nutrient for plant growth. NH3 can be directly applied to soil or used to produce other nitrogen fertilizers like urea. The other options (CO, O3, CO2) are not used as fertilizers - CO is toxic, O3 is an air pollutant at ground level, and CO2 is not a direct fertilizer though plants need carbon.