Question

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 ($\alpha$ for copper = $1.7\times {10}^{-5}{/}^{\circ }C$ and $\alpha$ for steel = $1.1\times {10}^{-5}{/}^{\circ }C$) -

• A. 9.17 cm; 14.17 cm
• B. 9.02 cm; 14.20 cm
• C. 9.08 cm; 14.08 cm
• D. 9.50 cm; 14.50 cm

Answer 1

The correct option is A

9.17 cm; 14.17 cm

Let $L_S$ and $L_C$ be the lengths of the steel and copper rods, and ${\alpha }_S$ and ${\alpha }_C$ be their coefficients of linear expansion respectively. When the rods are heated by $\Delta T^{\circ }C$, the increases in lengths of the steel rod and the copper rod, are

$\Delta L_S$ = $L_S{\alpha }_S\Delta T$,

$\Delta L_C$ = $L_C{\alpha }_C\Delta T$.

Given $L_S$ - $L_C$ = 5cm for all $\Delta T$,

$L_S{\alpha }_S\Delta T$ = $L_C{\alpha }_C\Delta t$

$\frac{L_S}{L_C}$ = $\frac{{\alpha }_C}{{\alpha }_S}$ = $\frac{1.7\times {10}^{-5}}{1.1\times {10}^{-5}}$

$L_S$ = $\frac{17L_C}{11}$.

Using this in ($L_S-L_C$) = 5, and solving, we get $L_C$ = 9.17 cm.

Therefore, $L_S$ = 5 + 9.17 = 14.17 cm.

Hence (A) is correct