The spring constant of a spring depends on its

[amp_mcq option1=”length only” option2=”material only” option3=”length and its diameter” option4=”thickness, its diameter and its material” correct=”option4″]

This question was previously asked in

UPSC CDS-2 – 2016

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The spring constant of a spring depends on its physical and material properties including its thickness, diameter, and material.

– The spring constant (k) quantifies the stiffness of a spring.
– For a helical spring, the spring constant is given by the formula k = (G * d⁴) / (8 * D³ * n), where G is the shear modulus of the material, d is the wire diameter (thickness), D is the coil diameter, and n is the number of active turns (related to length).
– Therefore, k depends on the material (shear modulus G), the wire thickness (d), the coil diameter (D), and the number of turns (n, which determines the overall length for a given coil diameter and pitch).
– Option D includes thickness (wire diameter), diameter (coil diameter), and material, which are the key determinants of the spring constant.

The spring constant is an intrinsic property of a specific spring configuration. Changing any of these physical parameters will change the spring constant. For example, a thicker wire makes the spring stiffer (higher k), a larger coil diameter or more turns make it less stiff (lower k), and using a material with a higher shear modulus makes it stiffer.

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