Core Formula/Logic: Classification based on measurement units: length vs. area.
Step-by-Step Solution: 1. Identify what each option measures. 2. Metre, furlong, and mile are all units of length or distance. 3. Acre is a unit of area. 4. Therefore, acre is the odd one out.
Common Pitfall: Confusing acre with length units or not recognizing that furlong and mile are both imperial length units like metre is metric length.
Shortcut/Takeaway: In classification questions, first determine the common category for most items; the one that doesn't fit that category is the odd one. Remember: acre measures land area, while others measure linear distance.

Why Correct: Radian measures plane angle, not length. The SI defines radian as the angle subtended at a circle's center by an arc equal in length to the radius.
Distractor Analysis: Light year equals the distance light travels in one year in vacuum, approximately 9.46 trillion kilometers. Micron is a metric unit equal to one millionth of a meter (1 μm = 10^-6 m). AU (astronomical unit) represents the average Earth-Sun distance, about 149.6 million kilometers.
Takeaway: The SI base unit for length is meter, with derived units like kilometer (10^3 m), centimeter (10^-2 m), and millimeter (10^-3 m).

Core Formula/Logic: Newton's law of gravitation: F = G m1 m2 / r2. Dimensions: [G] = [F][r2] / [m1][m2].
Step-by-Step Solution: 1. Force F has dimensions [M L T-2].
2. Distance r has dimensions [L], so r2 has [L2].
3. Mass m1 and m2 each have dimensions [M], so m1 m2 has [M2].
4. Therefore, [G] = ([M L T-2] × [L2]) / [M2] = [M-1 L3 T-2].
5. In CGS units: M → gm, L → cm, T → sec, so dimensions are [gm-1 cm3 sec-2], which matches cm3 sec-2 gm-1.
Common Pitfall: Misplacing mass exponent as -2 gives gm-2 cm3 sec-2 (not listed). Forgetting to square r yields cm sec-2 gm-1, producing option B.
Shortcut/Takeaway: Memorize [G] = [M-1 L3 T-2]. In CGS, it's always gm-1 cm3 sec-2, with mass in denominator and length cubed in numerator.

Why Correct: Picometer is a unit of length equal to 10^-12 meters, not a measuring instrument.
Distractor Analysis: Barometer measures atmospheric pressure. Thermometer measures temperature. Hygrometer measures humidity or moisture content in the air.
Takeaway: Common measuring instruments include anemometer (wind speed), manometer (pressure), and calorimeter (heat measurement).

Why Correct: An ordinary balance compares an unknown mass with known standard masses using gravitational force, directly measuring mass which remains constant regardless of location.
Distractor Analysis: Volume measures three-dimensional space occupied by a substance. Weight measures gravitational force on a mass and varies with location. Density measures mass per unit volume and requires both mass and volume measurements.
Takeaway: Spring scales measure weight, while balances measure mass by comparison; this distinction becomes crucial in physics problems involving different gravitational environments.

Why Correct: The SI system has exactly two supplementary units: the radian (rad) for plane angle and the steradian (sr) for solid angle.
Distractor Analysis: 3 and 4 are incorrect counts that don't match any SI classification. Many incorrectly suggests an indefinite number, but supplementary units are precisely defined.
Takeaway: Since 2019, the SI redefined supplementary units as derived units with special names, but exam questions often still test the traditional count of two supplementary units.