Question

Linear mass density of a rod varies as lambda=Kx. Among the axes shown, the moment of inertia of the rod is
maximum for
(1) AA
(3) BB
В
С
(2) CC
(4) None of these​

Answer 1

answer : option (2) CC'

explanation : Let moment of inertia of rod will be maximum about at an axis which is x distance from origin (AA').

now, mass of element , dm = λdx = kx dx

now, moment of inertia of element about an axis passing through origin, (AA') , dI = dm x²

⇒∫dI =∫ (kx)(x²)dx

⇒I = k ∫x³ dx

⇒I = kx⁴/4

hence, I is directly proportional to x⁴,

so, higher the value of x, higher will be moment of inertia.

as value of x = 2 is higher than that of x = 0 and x = 1

so, moment of inertia will be maximum about an axis passing through at x = 2 i.e., CC'

hence, option (2) is correct choice.

Answer 2

Explanation:

Mass is concentrated at x = 2 ( cc') axis . But if we take that axis r will become very less . So we choose aa' axis so that distance will become max and thus max moment of inertia.

THEREFORE ANSWER WOULD BE (1)