The moment of inertia of a body is I and its coefficient of linear expansion is α if the temperature of the body rises by a small amount Δ T . Then change in the moment of inertia about the same axis is

Question

The moment of inertia of a body is I and its coefficient of linear expansion is α if the temperature of the body rises by a small amount Δ T . Then change in the moment of inertia about the same axis is (A) α IΔ T (B) 2α IΔ T (C) 4α IΔ T (D) (α I Δ T/2)

Tardigrade Admin · Accepted Answer

The expression of the moment of inertia of a body is

I \propto m r^{2} \Rightarrow I = km r^{2}

and thermal expansion in dimension,

Δ r = r α Δ T

Now, fractional change in moment of inertia due to thermal expansion,

\frac{Δ I}{I} = \frac{2Δ r}{r} = 2 α Δ T

or

Δ I = 2 α I Δ T

Q. The moment of inertia of a body is $I$ and its coefficient of linear expansion is $α$ if the temperature of the body rises by a small amount $Δ T$ . Then change in the moment of inertia about the same axis is

$α I Δ T$

$2 α I Δ T$

$4 α I Δ T$

$\frac{α I Δ T}{2}$

The expression of the moment of inertia of a body is
$I \propto m r^{2} \Rightarrow I = km r^{2}$
and thermal expansion in dimension, $Δ r = r α Δ T$
Now, fractional change in moment of inertia due to thermal expansion, $\frac{Δ I}{I} = \frac{2Δ r}{r} = 2 α Δ T$
or $Δ I = 2 α I Δ T$

Q. The moment of inertia of a body is I and its coefficient of linear expansion is α if the temperature of the body rises by a small amount ΔT . Then change in the moment of inertia about the same axis is

αIΔT

2αIΔT

4αIΔT

2αIΔT​