Core Formula/Logic: Weight = mass × gravitational acceleration (g). At Earth's center, gravitational acceleration becomes zero because mass pulls equally in all directions.
Step-by-Step Solution: 1. Weight depends on gravitational force: W = m × g. 2. At Earth's center, the net gravitational force is zero (g = 0). 3. Therefore, W = m × 0 = 0.
Common Pitfall: Confusing weight with mass produces 10 kg. Assuming halved gravity gives 5 kg. Thinking gravitational force becomes infinite at the center yields Infinite.
Shortcut/Takeaway: Weight is zero at Earth's center regardless of surface weight. Mass remains constant, but gravitational acceleration cancels out completely.

Why Correct: Weight equals gravitational force, which follows Newton's law of universal gravitation: F = G * (m1 * m2) / r^2. As distance r from Earth's center increases, gravitational force decreases.
Distractor Analysis: Increase would occur only if gravitational force strengthened with distance, which contradicts physics. Remain same would require gravitational force to be independent of distance, which only holds for uniform gravitational fields. Fluctuate suggests periodic or irregular changes, but weight decreases monotonically with altitude.
Takeaway: Weight becomes zero at infinite distance from Earth, but apparent weightlessness occurs in free-fall orbits where gravitational force still exists but is balanced by centripetal acceleration.

Why Correct: Acceleration due to gravity decreases with altitude because gravitational force follows Newton's inverse square law: g = GM/r2, where r is distance from Earth's center.
Distractor Analysis: Increases contradicts the inverse square relationship where gravity weakens with distance. Remains constant only approximates small altitude changes near Earth's surface where variation is negligible. None of the above is incorrect since the established physical law confirms the decrease.
Takeaway: At Earth's surface, g ≈ 9.8 m/s2; at altitude equal to Earth's radius (6371 km), g reduces to about 2.45 m/s2.

Why Correct: Kepler's third law for circular orbits gives T = 2π√(r³/GM), where r is distance from Earth's center, so period depends on orbital radius.
Distractor Analysis: is proportional to its distance from the earth’s centre is incorrect—period is proportional to r^(3/2), not r. is inversely proportional to its mass is wrong—satellite mass cancels in orbital equations. 24 hours applies only to geostationary satellites at specific altitude.
Takeaway: Geostationary satellites orbit at ~35,786 km altitude with 24-hour period, matching Earth's rotation for fixed positioning.

Why Correct: Earth's gravitational acceleration (9.8 m/s2) is about six times stronger than the moon's (1.6 m/s2), so escaping Earth's gravity requires the most energy.
Distractor Analysis: Landing on the moon uses energy for braking but benefits from the moon's weaker gravity. Rising from the moon requires escaping its much weaker gravitational field. Landing on Earth uses atmospheric drag and parachutes, converting kinetic energy to heat rather than requiring propulsive energy.
Takeaway: The energy required to escape a celestial body depends on its escape velocity, which equals sqrt(2GM/r) where G is the gravitational constant, M is the mass, and r is the radius.

Why Correct: Gravitational force is the weakest fundamental force, with a relative strength of about 10^-39 compared to the strong nuclear force.
Distractor Analysis: Electromagnetic force governs interactions between charged particles and is 10^36 times stronger than gravity. Nuclear force binds protons and neutrons in atomic nuclei and is the strongest fundamental force. Electrostatic force is a manifestation of electromagnetic force between stationary charges.
Takeaway: The four fundamental forces from weakest to strongest are: gravitational, weak nuclear, electromagnetic, and strong nuclear.

Core Formula/Logic: Weight = mass × gravitational acceleration (W = m×g). Moon's gravity is approximately 1/6th of Earth's gravity (g_moon ≈ g_earth/6 ≈ 1.63 m/s2).
Step-by-Step Solution: 1. Mass remains constant everywhere: m = 12 kg.
2. Weight on Earth: W_earth = 12 kg × g_earth.
3. Weight on Moon: W_moon = 12 kg × (g_earth/6) = (12 kg × g_earth)/6 = W_earth/6.
4. Since W_earth = 12 kg-weight (not mass), W_moon = 12/6 = 2 kg-weight.
Common Pitfall: Confusing mass (constant) with weight (varies with gravity) leads to selecting 12 kg. Thinking gravity differences are smaller (like 3/4) produces 9 kg. Multiplying instead of dividing gives 18 kg.
Shortcut/Takeaway: Moon weight = Earth weight ÷ 6. Always divide Earth weight by 6 for lunar weight calculations.