माना कि दो धातु के घनों P और Q के क्रमशः x, y आयतन हैं; m, n द्रव्यमान हैं। Q की प्रत्येक भुजा P की दोगुनी है और Q का द्रव्यमान P का दोगुना है। माना कि u = m / x और v = n / y है। निम्नलिखित में से कौन-सा सही है?
Read this question in English
Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?
(a) u = 4v · (b) u = 2v · (c) v = u · (d) v = 4u
उत्तर और व्याख्या · explanation in English
Answer: (a) u = 4v
Doubling the side multiplies a cube's volume by 2³ = 8, while the mass only doubles. So Q's mass per unit volume is 2/8 = 1/4 of P's, i.e. u = 4v.
- Side of Q = 2 × side of P, so y = 2³ x = 8x.
- n = 2m.
- v = n/y = 2m/8x = (1/4)(m/x) = u/4.
- So u = 4v.
Remember · Scaling a length by k scales volume by k³; compare ratios by writing each in terms of the smaller object.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·