(a)(i) The spring C has been stretched past the limit of proportionality.
(ii) Spring stretched within the limit of proportionality is equal to the increase in weight and in turn increase in the length of spring.
(iii) The un-stretched length of spring A is 4.5 cm.
The weight of any object is the mass times the acceleration due to gravity on Earth or any other planet.
Weight W = mg
where g = 9.81 m/s²
Given, a student has three springs A, B and C. He measures the length of each spring, in turn, when different weights are placed on the end of each spring. His table of results is shown in Figure.(a)
(i) The spring C has been stretched past the limit of proportionality.
(ii) Spring stretched within the limit of proportionality is equal to the increase in weight and in turn increase in the length of spring.
In case of spring C, there is an unequal increase in weight and length of spring of 0.8 cm, when weight change from 1 to 1.5 N and 1.8 cm increase , when weight change from 2 to 2.5 N.
(iii) The natural length of spring be Xo and X is the increase in length due to 1N weight.
So, the equations formed will be
Xo + X = 6.1 cm....................(1)
Xo + 2X = 7.7 cm....................(2)
Solving both the equations, we get
X = 1.6 cm and Xo = 4.5 cm
Thus, the un-stretched length of spring A is 4.5 cm.
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