$A$ circular disc with a hole is shown in the figure. On heating,if the outer diameter $d_1$ increases by $0.3\%$,then the inner diameter $d_2$ will

  • A
    Decrease by $0.1\%$
  • B
    Decrease by $0.3\%$
  • C
    Increase by $0.1\%$
  • D
    Increase by $0.3\%$

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$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

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