When the temperature of a straight rigid rod increases from t to t- t- its moment of inertia changes from I to I- I- If - be the coefficient of linear expansion- then 2- -t will be equal to-

The correct option is B Δ I/I The moment of inertia of a rod is given by I=ML^2/12 So, Δ I/I=2Δ L/L nbsp; nbsp; nbsp; nbsp; nbsp; nb ...

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Byju's Answer

Standard XII

Physics

Thermal Expansion

When the temp...

Question

When the temperature of a straight rigid rod increases from t to $t + Δ t$ , its moment of inertia changes from I to $I + Δ I$ . If $α$ be the coefficient of linear expansion, then $2 α$ $Δ$ t will be equal to.

\frac{I}{Δ I}

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I \times Δ I

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\frac{Δ I}{I}

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2 I Δ I

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Solution

The correct option is B $\frac{Δ I}{I}$
The moment of inertia of a rod is given by
$I = \frac{M L^{2}}{12}$
So, $\frac{Δ I}{I} = \frac{2 Δ L}{L}$ .......(i)
Also, linear expansion of rod is given by
$Δ L = L α Δ t$
From Eq. (i), $\frac{Δ I}{I} = 2 \frac{L α Δ t}{L} = 2 α Δ t$
So, $2 α Δ t = \frac{Δ I}{I}$ .

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When the temperature of a straight rigid rod increases from t to t+Δt, its moment of inertia changes from I to I+ΔI. If α be the coefficient of linear expansion, then 2α Δt will be equal to.

The correct option is B ΔIIThe moment of inertia of a rod is given byI=ML212So, ΔII=2ΔLL .......(i)Also, linear expansion of rod is given byΔL=LαΔtFrom Eq. (i), ΔII=2LαΔtL=2αΔtSo, 2αΔt=ΔII.

When the temperature of a straight rigid rod increases from t to $t + Δ t$ , its moment of inertia changes from I to $I + Δ I$ . If $α$ be the coefficient of linear expansion, then $2 α$ $Δ$ t will be equal to.