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

Span of bridge = 2400 m and bridge sags by 500 m at 30° (given)From Fig., LPRQ = 212002+5002= 2600 mBut L = L0(1 +αΔt)                         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           ΔL= 2599 × 12 × 10−6× 42 − 10 = 0.99m