Question

A metal rod having a coefficient of linear
expansion of 2 x 10-5 °C has a length of
100 cm at 20 °C. The temperature at which it
is shortened by 1mm is
(A) - 40°C
(B) – 30 °C
1C) -20 °C
(D) -10°C​

Answer 1

Answer:

option (B) –30°C

Explanation:

Given :

A metal rod having a coefficient of linear  expansion of 2 x 10⁻⁵ /°C has a length of  100 cm at 20°C.

To find :

the temperature at which it  is shortened by 1 mm

Solution :

we know,

  $\underline{\boxed{\bf \Delta l=l \alpha \Delta t}}$

where

Δl denotes change in length

l denotes the initial length

α denotes the coefficient of linear expansion

Δt denotes the temperature difference

Let the temperature at which the rod is shortened by 1 mm be t₂

here,

Δl = l₂ - l = -1 mm = -10⁻³ m [ -ve as the rod is shortened ]

l = 100 cm = 1 m

α = 2 × 10⁻⁵ /°C

Δt = (t₂ - 20)°C

Substitute the values,

-10⁻³ = 1 × 2 × 10⁻⁵ × (t₂ - 20)

t₂ - 20 = -10⁻³/2 × 10⁻⁵

t₂ - 20 = -0.5 × 10²

t₂ - 20 = -50

t₂ = -50 + 20

t₂ = -30°C

Therefore, the required temperature is -30°C