First slide

Moment of intertia

Question

From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius nr. If the M.I. of Q about its axis is four times that of P about its axis (assuming the wire to be of diameter much smaller than either radius), the value of n is

Moderate

A

${(4)}^{\frac{2}{3}}$
B

${(4)}^{\frac{1}{3}}$
C

${(4)}^{\frac{1}{2}}$
D

${(4)}^{\frac{1}{4}}$

Solution

$G i v e n t h a t I_{Q} = 41_{P}$ , Here I = mass x (radius $)^{2}$ . If s is the linear mass density (mass/ length) of the wire,
$σ \times 2 π (n r) \times n^{2} r^{2} = 4 (σ \times 2 π r \times r^{2})$ $\Rightarrow n^{3} = 4$

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