Span of a bridge is $$2.4$$ km. At $$30$$°C a cable along the span sags by $$0.5$$ km. Taking a $$=$$ $$12$$ × $$10-6/$$°C, change in length of cable for a change in temperature from $$10$$°C to $$42$$°C is

Question

Span of a bridge is $$2.4$$ km. At $$30$$°C a cable along the span sags by $$0.5$$ km. Taking a $$=$$ $$12$$ × $$10-6/$$°C, change in length of cable for a change in temperature from $$10$$°C to $$42$$°C is

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Span of bridge $$=$$ $$2400$$ m and bridge sags by $$500$$ m at $$30$$° (given)From$$ Fig., LPRQ $$=$$ $$212002+5002=$$ $$2600$$ mBut L $$=$$ $$L0(1$$ $$+$$αΔ$$t)                         Due to linear expansion           ⇒ $$2600$$ $$=$$ $$L0l$$ $$+$$ $$12$$ × $$10$$−$$6$$× $$30$$           Length of the $$cableL0=2599$$ m           Now change in length of cable due to change in tempera­ture from $$10$$°C to $$42$$°C           Δ$$L=$$ $$2599$$ × $$12$$ × $$10$$−$$6$$× $$42$$ − $$10$$ $$=$$ $$0.99m$$

Span of a bridge is 2.4 km. At 30°C a cable along the span sags by 0.5 km. Taking a = 12 × $10^{- 6}$ /°C, change in length of cable for a change in temperature from 10°C to 42°C is

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Span of a bridge is 2.4 km. At 30°C a cable along the span sags by 0.5 km. Taking a = 12 × 10-6/°C, change in length of cable for a change in temperature from 10°C to 42°C is

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Span of a bridge is 2.4 km. At 30°C a cable along the span sags by 0.5 km. Taking a = 12 × $10^{- 6}$ /°C, change in length of cable for a change in temperature from 10°C to 42°C is