Question: 40: Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements, choose the most appropriate answer from the options given below
(1) (A) is true but (R) is false
(2) (A) is false but (R) is true
(3) Both (A) and (R) are true and (R) is the correct explanation of (A)
(4) Both (A) and (R) are true and (R) is not the correct explanation of (A)
Answer: Option (1)
Explanation:
When a helical spring is stretched by an applied force,
the wire of the spring undergoes twisting rather than simple stretching.
The restoring force of a spring and hence its extension depends on the rigidity or
shear modulus of the material from which the spring is made.
Therefore, the stretching of a spring is determined by the shear modulus of the material,
making Assertion (A) true.
Tensile strength refers to the maximum stress a material can withstand before breaking,
and it is not directly related to the elastic behavior governing spring extension.
Steel has much higher tensile strength than copper for the same dimensions,
so the statement that a copper spring has more tensile strength than a steel spring is incorrect.
Hence, Reason (R) is false.
Therefore, the correct option is (1),
where Assertion (A) is true but Reason (R) is false.