A metal rod having linear expansion coefficient 2× 10- 5 ° C- 1 has a length of 1 m at 20 ° C . The temperature at which it is shortened by 1 mm is

Question

A metal rod having linear expansion coefficient 2× 10- 5 ° C- 1 has a length of 1 m at 20 ° C . The temperature at which it is shortened by 1 mm is (A) -20° C (B) -15° C (C) -30° C (D) -25° C

Tardigrade Admin · Accepted Answer

From, l2=l1[1 + α (t2 - t1)] t2=t1+(l2 - l1/l1 α ) = 20+(- 10- 3/1 .0 × 2 × 10- 5)=-30° C

Q. A metal rod having linear expansion coefficient $2 \times 1 0^{- 5}^{\circ} C^{- 1}$ has a length of $1 m$ at $20^{\circ} C$ . The temperature at which it is shortened by $1 mm$ is

$- 2 0^{\circ} C$

$- 1 5^{\circ} C$

$- 3 0^{\circ} C$

$- 2 5^{\circ} C$

From, $l_{2} = l_{1} [1 + α (t_{2} - t_{1})]$
$t_{2} = t_{1} + \frac{l _{2} - l _{1}}{l _{1} α}$
= $20 + \frac{- 1 0 ^{- 3}}{1.0 \times 2 \times 1 0 ^{- 5}} = - 3 0^{\circ} C$

Q. A metal rod having linear expansion coefficient 2×10−5∘C−1 has a length of 1m at 20∘C . The temperature at which it is shortened by 1mm is

−20∘C

−15∘C

−30∘C

−25∘C