Science and Technology Fundamentals

One orbit around the sun (a tropical year) takes approximately 365.2422 days, which is slightly less than 365 1/4 (365.25) days. The difference is why our calendar skips leap years on century years not divisible by 400. The 365 1/4 approximation was used in the Julian calendar but was slightly too long.

Earth's actual rotation period (sidereal day) is approximately 23 hours, 56 minutes, and 4 seconds, which is less than 24 hours. The 24-hour solar day is slightly longer because Earth must rotate a bit extra to face the sun again due to its orbital motion. This is why stars rise about 4 minutes earlier each night.

Leap years occur less often than once every 4 years because century years (1700, 1800, 1900) are NOT leap years unless divisible by 400 (1600, 2000). This Gregorian calendar rule averages to 97 leap days in 400 years, not 100. The answer 'less than once in every 4 years' correctly captures this nuance.

The Gregorian calendar is the western calendar used globally today, introduced by Pope Gregory XIII in 1582 to reform the Julian calendar. The Julian calendar was its predecessor but had too many leap years. The Roman calendar was even earlier and less sophisticated. There is no 'International calendar' as a formal name.

Northern hemisphere summer is slightly longer than southern hemisphere summer. This is because Earth is closer to the sun (perihelion) in January, during southern summer, making it move faster and shortening that season. Conversely, Earth is farther (aphelion) in July during northern summer, moving slower and lengthening it. The difference is several days.

Van der Waals forces (intermolecular attractions and repulsions) cause real gases to deviate from ideal gas behavior, especially at high pressure and low temperature. Ideal gas assumptions neglect molecular size and intermolecular forces.

Boyle's Law (1662) states that for a fixed amount of ideal gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂, or PV = constant. Option B confuses volume with temperature, while C incorrectly specifies real gases.

The Biot-Savart Law (1820) quantitatively describes the magnetic field contribution from a current element: dB = (μ₀/4π) · I dl × r̂ / r². Kirchhoff's laws govern circuit behavior, Dulong-Petit law concerns heat capacity, and Charles' law is a gas law.

The statement is false because it has the shifts reversed. Objects approaching the observer produce blueshift (higher frequency), while receding objects produce redshift (lower frequency).

Stefan-Boltzmann Law (1879-1884) states that total radiated power P = σAT⁴, where σ is Stefan-Boltzmann constant (5.67×10⁻⁸ W·m⁻²·K⁻⁴), A is surface area, T is absolute temperature in Kelvin. The T⁴ dependence is key.

Coulomb's Law (1785) is the fundamental law of electrostatics, quantifying force between electric charges: F = k(q₁q₂/r²)r̂, where k = 1/4πε₀. Charles' law is a gas law, Chandrasekhar limit concerns stellar astrophysics, and Coanda effect is fluid dynamics.

Gauss's law states that the electric flux through any closed surface is proportional to the enclosed electric charge. The differential form is ∇·E = ρ/ε₀.

Astronauts appear weightless not because gravity is absent, but because they are in continuous free fall around the Earth. At geostationary orbit altitude (approximately 35,786 km), gravitational force is still about 89% of what it is on Earth's surface. The sensation of weightlessness comes from the fact that both the astronaut and the spacecraft are falling at the same rate, creating the floating effect.

Average velocity is displacement divided by time, and displacement is the straight-line distance between initial and final positions. In a complete circular trip, the initial and final positions are the same, so displacement is zero, making average velocity zero. This is different from average speed, which would be non-zero since it's total distance traveled divided by time.

All elements can exist in all three states (solid, liquid, gas) given appropriate temperature and pressure conditions. Iron has a boiling point of 2862°C (5184°F), so it can indeed exist as a gas when heated above this temperature. While we typically encounter iron as a solid in everyday conditions, it transitions to liquid and gas phases at extremely high temperatures.

Technetium (atomic number 43) was the first element to be produced artificially in 1937 by Carlo Perrier and Emilio Segrè. All naturally occurring technetium on Earth comes from spontaneous fission of uranium-238 or from cosmic ray interactions. It was named from the Greek 'technetos' meaning 'artificial.' Molybdenum (42) and Protactinium (91) occur naturally, while Meitnerium (109) was synthesized much later in 1982.

Chandrayaan-1, India's first lunar mission, was successfully launched on October 22, 2008. The mission was launched by ISRO using a PSLV-XL rocket from the Satish Dhawan Space Centre in Sriharikota. This marked a significant milestone in India's space exploration program.

Chandrayaan-1 was indeed India's first mission to the moon. Before this, India had not sent any spacecraft to the moon. The statement is factually correct as Chandrayaan-1 marked India's entry into lunar exploration in 2008.

M3 stands for Moon Mineralogy Mapper, which was one of the key scientific instruments on Chandrayaan-1. It was a NASA instrument that helped map the mineral composition of the lunar surface and contributed to the discovery of water molecules on the moon.