When the temperature of a rod increases from t to t+Δ t, its moment of inertia increases from I to I+Δ I .If α be the coefficient of linear expansion of the rod, then the value of (Δ I/I) is

Question

When the temperature of a rod increases from t to t+Δ t, its moment of inertia increases from I to I+Δ I .If α be the coefficient of linear expansion of the rod, then the value of (Δ I/I) is (A)  2α Δ t  (B)  α Δ t  (C)  (α Δ t/2)  (D)  ( Δ t/α )

Tardigrade Admin · Accepted Answer

Moment of inertia of a rod I=(Mλ 2/12) dI=(M/12)2λ dλ (dI/I)=2(dλ /λ )=2α Δ t

Q. When the temperature of a rod increases from t to $t + Δ t,$ its moment of inertia increases from $I$ to $I + Δ I$ .If $α$ be the coefficient of linear expansion of the rod, then the value of $\frac{Δ I}{I}$ is

$2 α Δ t$

$α Δ t$

$\frac{α Δ t}{2}$

$\frac{Δ t}{α}$

Moment of inertia of a rod $I = \frac{M λ ^{2}}{12}$ $d I = \frac{M}{12} 2 λ d λ$ $\frac{d I}{I} = 2 \frac{d λ}{λ} = 2 α Δ t$

Q. When the temperature of a rod increases from t to t+Δt, its moment of inertia increases from I to I+ΔI .If α be the coefficient of linear expansion of the rod, then the value of IΔI​ is

2αΔt

αΔt

2αΔt​

αΔt​