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

Span of bridge = 2400 m and bridge sags by 500 m at 30o (given) From figure, LPRQ=212002+5002=2600m But  L=L0(1+αΔt)     (Due to linear expansion)⇒ 2600=L01+12×10−6×30∴  Length of the cable L0=2599mNow change in length of cable due to change in temperature from 10oC to 42oCΔL=2599×12×10−6×(42−10)=0.99m