Question

Two circular loop A and B of radii Rand NR respectively are made from a uniform wire. Moment of inertia of B about its axis is 3 times that of A about its axis. The value of N is ______.

पर्याय

• `[2]^(1/3)`

• `[5]^(1/3)`

• `[3]^(1/3)`

• `[4]^(1/3)`

Answer 1

Two circular loop A and B of radii Rand NR respectively are made from a uniform wire. Moment of inertia of B about its axis is 3 times that of A about its axis. The value of N is `underline([3]^(1/3))`.

Explanation:

Given, r_A = R and r_B = NR

Mass of wire A, m_A = 2πr_A ρ = 2πRρ

Mass of wire B, m_B = 2πr_B ρ = 2πNRρ = Nm_A

The moment of inertia of a circular loop is

I = mr²

Here, I_B = 3I_A

`=> "m"_"B""r"_"B"^2 = 3 xx "m"_"A""r"_"A"^2`

`=> "Nm"_"A" ("NR")^2 = 3"m"_"A"("R")^2`

`=> "N"^3 = 3` or N = (3)^1/3