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Area and Volume Expansion

A circular di...

Question

A circular disc has a hole of diameter $d_{1}$ and an external diameter $d_{2}$ , where $d_{2} = 3 d_{1}$ . On heating $d_{2}$ increases by $0.3$ %. Find $d_{1}$ .

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Solution

Circular disc which has a whole of distance $= d_{1}$
External distance $= d_{2}$
Given, $d_{2} = 3 d_{1}$
As per question,
$I n i t i a l d_{2} F i n a l d_{2} 100100 - 3 d_{2} ? ∴ F i n a l d_{2} = \frac{100 - 3 \times d_{2}}{100} d_{1} = \frac{d_{2}}{3} \to (1)$
For final value of $d_{2} = \frac{100 - 3 d_{2}}{100}$
On putting in equation $(1)$ and we will get,
$d_{1} = \frac{100 - 3 d_{2}}{100 \times 3} d_{1} = 0.334 d_{2}$

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