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 ✓ UPSC's answer
- (b) u = 2v
- (c) v = u
- (d) v = 4u
Why the answer is (a)
• Let each side of P be a. Then x = a³ and m is its mass.
• Each side of Q is 2a, so y = (2a)³ = 8a³, and its mass n = 2m.
• u = m/a³ and v = 2m/8a³ = m/(4a³) = u/4.
• So u = 4v — option (a).
Why the other options are wrong
- (b) u = 2v
- This takes the volume ratio as 2 instead of 8; Q's volume is 8 times P's, so u = 4v.
- (c) v = u
- The two densities are not equal: Q has twice the mass but eight times the volume.
- (d) v = 4u
- This reverses the relation; u is four times v, not the other way round.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.