The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C

Solution:

It is given that when C = 20, the value of L = 124.942, whereas when C = 110, the value of L = 125.134.

Accordingly, points (20, 124.942) = (x₁, y₁) and (110, 125.134) = (x₀, y₂) satisfy the linear relation between L and C

Now, assuming C along the x-axis and L along the y-axis, we have two points i.e., (20, 124.942) and (110, 125.134) in the XY plane.

Therefore, the linear relation between L and C is the equation of the line passing through points (20, 124.942) and (110, 125.134) and it can be found using the formula,

(L - y₁ = (y₂ - y₁ / (x₂ - x₁) (x - x₁)

(L - 124.942) = (125.134 - 124.942)/(110 - 20) (C - 20)

(L - 124.942) = 0.192/90 (C - 20)

L = 0.192/90 (C - 20) + 124.942

Thus, the required linear relation is L = 0.192/90 (C - 20) + 124.942

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 16

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C

Summary:

The length L (in centimetre) of a copper rod in terms of Celsius temperature C is, L = 0.192/90 (C - 20) + 124.942