Question

A close-coiled helical spring shown below in Fig-I is to be cut into two equal pieces and combined as a parallel spring as shown in Fig-II. The ratio shown in Fig-II to that of Fig-I, due to the same load W will be

• A. 1
• B. 1/2
• C. 1/4
• D. 1/8

Answer 1

The correct option is C 1/4

Angular twist in a spring is

$\theta =\frac{32WRL}{\pi d^{4}G}$

where

d is diameter of wire of spring
G is modulus of rigidity
W is axial pull on spring
R is mean radius of coil
L is Length of spring

$\therefore \frac{{\theta }_2}{{\theta }_1}=\frac{W_2}{W_1}\times \frac{L_2}{L_1}$

$=\frac{W/2}{W}\times \frac{L/2}{L}=\frac{1}{4}$