Two metal rods have coefficients of linear expansion 1-1 - 10-5- C and 1-65 - 10-5- C respectively- The difference in lengths is 10 cm at all temperatures- Their initial lengths must be respectively -

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Byju's Answer

Standard XII

Physics

Projectile from a Height

Two metal rod...

Question

Two metal rods have coefficients of linear expansion $1.1 \times 10^{- 5} /^{\circ} C$ and $1.65 \times 10^{- 5} /^{\circ} C$ respectively. The difference in lengths is 10 cm at all temperatures. Their initial lengths must be respectively :

40 cm and 50 cm

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40 cm and 30 cm

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50 cm and 60 cm

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30 cm and 20 cm

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Solution

The correct option is B 30 cm and 20 cm
since the difference in length for both the rods are same always, we can write,
$α_{1} l_{1} = α_{2} l_{2}$
$l_{1} / l_{2} = α_{2} / α_{1}$
or, $(l_{1} - l_{2}) / l_{2} = (α_{2} - α_{1}) / α_{1}$ $=$ 0.55/1.1 $=$ 1/2
$(l_{1} - l_{2})$ $=$ 10 (given)
Calculating we ge $l_{1}$ $=$ 30 cm . So, $l_{2}$ $=$ 20 cm

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