Question

from a given sample of uniform wire, two circular loops PQ are made P of radius rQ of radius nr. if the moment of inertia of Q about its axis is 4 times that of P about its axis (assuming wire diameter much smaller than either radius) the value of n is

Answer 1

Let mass of loop P be 'm' then mass of loop Q 'nm"

MI of loop P = mr²

MI of loop Q = nm * (nr)²
= n³ * mr²

From, the condition given in the question
n³ * mr² = 4 mr²

or, n³ = 4

or, n = 4^1/3


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