$(a)\;2I_{0} \alpha \bigtriangleup t\qquad(b)\;I_{0} \alpha \bigtriangleup t\qquad(c)\;Depends\;on\;the\;value\;of\;'a'\qquad(d)\;None\;of\;these$

Thermodynamics

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Answer : $2I_{0} \alpha \bigtriangleup t$

Explanation :

$I_{0}=\large\frac{ma^2}{12}$

$a_{T}=a (1+\alpha \bigtriangleup t)$

$a_{T}^{2}=a (1+\alpha \bigtriangleup t)^2$

$\approx a^2 (1+2 \alpha \bigtriangleup t)$

$= {\bigtriangleup t \to 0}$

$I_{T}=\large\frac{ma^2(1+2 \alpha \bigtriangleup t)}{12}$

$I_{T}=I_{0} (1+2 \alpha \bigtriangleup t)$

Therefore , $\bigtriangleup I=2I_{0} \alpha \bigtriangleup t$

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