What should be length of Steel and Copper Rods at $0^{o} C$ that the length of steel is always $5 c m$ longer than copper, given $α$ for steel N Copper are $1.7 \times 10^{- 5}$ and $1.1 \times 10^{- 5}$

Open in App

Solution

For linear expansion of rods
$L = L_{o} (1 + α △ T)$
Let $L_{S}$ and $L_{C}$ be the lengths of steel and copper rods respectively.
The difference in the length remains constant if,
$\frac{L_{S}}{L_{C}} = \frac{α_{C}}{α_{S}} = \frac{17}{11} (1)$
Also, $L_{S} - L_{C} = 5 c m (2)$
From $(1)$ and $(2)$ , we get
Length of steel Rod $\Rightarrow L_{S} = 14.17 c m$
Length of Copper Rod $\Rightarrow L_{C} = 9.17 c m$

Suggest Corrections

Similar questions

Q. What should be lengths of steel and copper rod, so that the length of steel rod is

5 c m

longer than the copper rod at all temperature?

(α

for copper

= 1.7 \times 10^{- 5}^{\circ} C^{- 1}

and

α

for steel

= 1.1 \times 10^{- 5}^{\circ} C^{- 1})

Q. What should be lengths of steel and copper rod, so that the length of steel rod is

5 c m

longer than the copper rod at all temperatures? (

α

of copper

- 1.7 \times 10^{- 5}^{o} C^{- 1}

and

α

for steel

= 1.1 \times 10^{- 5}^{o} C^{- 1}

The lengths of steel and copper rods are so that the length of the steel rod is 5 cm longer than that of the copper rod at all temperatures, then length of each rod, are ( $α$ for copper = $1.7 \times 10^{- 5} /^{\circ} C$ and $α$ for steel = $1.1 \times 10^{- 5} /^{\circ} C$ ) -

What should be the length of aluminium and steel rod, so that steel rod is always 10 cm longer than aluminium, at all temperatures?

α_{A l} = 12 \times 10 - 5 /^{o} C

α_{S t e e l} = 7 \times 10 - 5 /^{o} C

Join BYJU'S Learning Program

What should be length of Steel and Copper Rods at 0oC that the length of steel is always 5cm longer than copper, given α for steel N Copper are 1.7×10−5 and 1.1×10−5

For linear expansion of rodsL=Lo(1+α△T)Let LS and LC be the lengths of steel and copper rods respectively.The difference in the length remains constant if,LSLC=αCαS=1711(1)Also, LS−LC=5cm(2)From (1) and (2), we getLength of steel Rod ⇒LS=14.17cmLength of Copper Rod ⇒LC=9.17cm

What should be length of Steel and Copper Rods at $0^{o} C$ that the length of steel is always $5 c m$ longer than copper, given $α$ for steel N Copper are $1.7 \times 10^{- 5}$ and $1.1 \times 10^{- 5}$