# 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 : **

# Two metallic cubes P and Q

Since each side of cube Q is two times that of cube P, the volume of Q will be 2^3 = 8 times that of P. This means y = 8x. Since the mass of Q is two times that of P, we have n = 2m. Now we can use these relationships to find the relationship between u and v.

u = m/x and v = n/y

Substituting n = 2m and y = 8x into v = n/y

gives us: v = (2m)/(8x) v = m/(4x)

Since u=m/x, we can see that u=4v.

So the correct answer is (a) u=4v.