Question

If a helical spring is halved in length, its spring stiffness remains:

• A. same
• B. halves
• C. doubles
• D. Triples

Hint:

For helical springs, stiffness is inversely proportional to the number of coils. Halving the spring length doubles the stiffness.

Answer 1

The Correct Option is C

Step 1: Spring Stiffness Formula
The stiffness \( k \) of a helical spring is defined by:\[k = \frac{Gd^4}{8nD^3}\]Where:- \( G \) represents the shear modulus,- \( d \) represents the wire diameter,- \( n \) represents the number of active coils,- \( D \) represents the mean coil diameter.Step 2: Impact of Halving Spring Length Reducing the spring's length by half also halves the number of active coils \( n \). Consequently, the spring stiffness doubles because stiffness is inversely proportional to the number of coils.Step 3: Summary In summary, halving the length of a helical spring results in a doubling of its stiffness. Final Answer: \[ \boxed{\text{Doubles}}\]