Ncert Exercises & Solutions

A student records the initial length l, change in temperature $∆$ T and change in length $∆$ l of a rod as follows.

If the first observation is correct, what can you say about observations 2, 3 and 4?

Hint: The coefficient of linear expansion will be the same in all the cases.

Step 1: Find the coefficient of linear expansion in the first case.

From the 1st observation,

α = \frac{∆ l}{l ∆ T} \Rightarrow α = \frac{4 \times 10^{- 4}}{2 \times 10} = 2 \times 10^{- 5} ° C^{- 1}

Step 2: Find the change in length in all other cases.

For 2nd observation,

∆ l = α l ∆ T

= 2 \times 10^{- 5} \times 1 \times 10 = 2 \times 10^{- 4} m

(Wrong)

For 3rd observation,

∆ l = α l ∆ T

= 2 \times 10^{- 5} \times 2 \times 20 = 8 \times 10^{- 4} m

(Wrong)

For 4th observation,

∆ l = α l ∆ T

= 2 \times 10^{- 5} \times 3 \times 10 = 6 \times 10^{- 4} m

[i.e., observed value (Correct)]