SATHEE: Properties Of Solids And Liquids Question 99

Properties Of Solids And Liquids Question 99

Question: A steel scale measures the length of a copper wire as $80.0 c m,$ when both are at $20^{\circ} C$ (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at $40^{\circ} C$ ? (Given asteel $= 11 \times 10^{- 6}$ per°C and acopper $= 17 \times 10^{- 6} p e r^{\circ} C$ ) [CPMT 2004]

Options:

A) $80.0096 c m$

B) $80.0272 c m$

C) $1 c m$

D) $25.2 c m$

Show Answer

Answer:

Correct Answer: A

Solution:

With temperature rise (same 25°C for both), steel scale and copper wire both expand.

Hence length of copper wire w.r.t. steel scale or apparent length of copper wire after rise in temperature $L_{a p p} = L_{c u}^{'} - L_{s t e e l}^{'} = [L_{0} (1 + α_{C u} Δ θ) - L_{0} (1 + α_{s} Δ θ)$

therefore $L_{a p p} = L_{0} (α_{C u} - α_{s}) Δ θ$

$= 80 (17 \times 10^{- 6} - 11 \times 10^{- 6}) \times 20$ = 80.0096 cm

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Properties Of Solids And Liquids Question 99

Question: A steel scale measures the length of a copper wire as 80.0cm, when both are at 20∘C (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at 40∘C ? (Given asteel =11×10−6 per°C and acopper =17×10−6per∘C ) [CPMT 2004]

Options:

Answer:

Solution:

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