Question

The density of a non-uniform rod of length 1m is given by ρ(x) = a(1 + bx²) where a and b are constants and 0 ≤ x ≤ 1. The centre of mass of the rod will be at

(A) 3(2 + b)/4(3 + b)

(B) 4(2 + b)/3(3 + b)

(C) 3(3 + b)/3(2 + b)

(D) 4(3 + b)/3(2 + b)

Answer 1

Correct option (A)

Explanation:

When b → 0, the density becomes uniform and hence the centre of mass is at x = 0.5. Only option (A) tends to 0.5 as b → 0