Question

Length of steel rod so that it is 5 cm longer than the copper rod at all temperatures should be ______ cm.

(α for copper = 1.7 × 10^-5/°C and α for steel = 1.1 × 10^-5/°C)

Options

• 11.23

• 14.17

• 12.55

• 16.55

Answer 1

Length of steel rod so that it is 5 cm longer than the copper rod at all temperatures should be 14.17 cm.

Explanation:

Let length of steel rod be = l_st

Let length of copper rod be = l_cu = l_cu

If temperature is increased by Δθ then,

l_st = l_st(1 + α_st Δθ)

l_su = l_cu(1 + α_cu Δθ)

l_st = l_cu = (l_st - l_cu) + (l_st α_st - l_cu α_cu)Δθ

But l_st - l_cu = l_st - l_cu

⇒ l_st α_st - l_cu α_cu = 0

(l_cu + 5) × 1.1 × 10^-5 = 1.7 × 10^-5 × l_cu

17 l_cu = 11 l_cu + 55

l_cu = `55/6` = 9.17 cm

l_st = l_cu + 5

= 9.17 + 5

= 14.17 cm