Q. 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 or the following is correct?
(a) u = 4v
(b) u = 2v
(c) v=u
(d) v = 4u
Correct Answer: (a) u = 4v
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Let x y be the volumes …
Let’s solve this step by step.
1) Let’s say the side length of cube P is ‘a’
Then volume of P (x) = a³
Mass of P is m
2) For cube Q:
Side length is 2a (given: each side of Q is two times that of P)
Volume of Q (y) = (2a)³ = 8a³
Mass of Q (n) = 2m (given: mass of Q is two times that of P)
3) Now, let’s calculate u = m/x
u = m/a³
4) Let’s calculate v = n/y
v = 2m/(8a³)
v = (2m)/(8a³)
v = m/(4a³)
v = (m/a³)/4
v = u/4
5) Therefore:
u = 4v
Looking at the options, (a) u = 4v is correct.
The answer is (a).
