When a close coiled helical spring is compressed, its wire is subjected to

When a closely-coiled helical spring of mean diameter (D) is subjected to an axial load (W), the deflection of the spring ($$\delta $$) is given by (where d = Diameter of spring wire, n = No. of turns of the spring and C = Modulus of rigidity for the spring material)

A

$$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$

B

$$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$

C

$$\frac{{4{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$

D

$$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{C}}{{\text{d}}^4}}}$$

When an open coiled helical compression spring is subjected to an axial compressive load, the maximum shear stress induced in the wire is (where D = Mean diameter of the spring coil, d = Diameter of the spring wire, K = Wahl's stress factor and W = Axial compressive load on the spring)

A

$$\frac{{{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

B

$$\frac{{2{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

C

$$\frac{{4{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

D

$$\frac{{8{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

Two closely-coiled helical springs 'A' and 'B' of the same material, same number of turns and made from same wire are subjected to an axial load W. The mean diameter of spring 'A' is double the mean diameter of spring 'B'. The ratio of deflections in spring 'B' to spring 'A' will be

A

$$\frac{1}{8}$$

B

$$\frac{1}{4}$$

C

2

D

4

A closely coiled helical spring is acted upon by an axial force. The maximum shear stress developed in the spring is $$\tau $$. The half of the length of the spring if cut off and the remaining spring is acted upon by the same axial force. The maximum shear stress in the spring in new condition will be

A

$$\frac{\tau }{2}$$

B

$$\tau $$

C

$$2\tau $$

D

$$4\tau $$

Two closely coiled helical springs 'A' and 'B' are equal in all respects but the diameter of wire of spring 'A' is double that of spring 'B' The stiffness of spring 'B' will be __________ that of spring 'A'

A

One-sixteenth

B

One-eighth

C

One-fourth

D

One-half

When a closely coiled helical spring is subjected to a couple about its axis, the stress induced in the wire material of the spring is

A

Bending stress only

B

A combination of torsional shear stress and bending

C

Direct shear stress only

D

A combination of bending stress and direct shear stress

Two closely coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is half that of spring 'B'. The ratio of deflections in spring 'A' to spring 'B' is

A

$$\frac{1}{8}$$

B

$$\frac{1}{4}$$

C

$$\frac{1}{2}$$

D

2

Two closely-coiled helical springs 'A' and 'B' are equal in all respects but the number of turns of spring 'A' is double that of spring 'B'. The stiffness of spring 'A' will be __________ that of spring 'B'.

A

One-sixteenth

B

One-eighth

C

One-fourth

D

One-half

When a closely-coiled helical spring of mean diameter (D) is subjected to an axial load (W), the stiffness of the spring is given by

A

$$\frac{{{\text{C}}{{\text{d}}^4}}}{{{{\text{D}}^3}{\text{n}}}}$$

B

$$\frac{{{\text{C}}{{\text{d}}^4}}}{{2{{\text{D}}^3}{\text{n}}}}$$

C

$$\frac{{{\text{C}}{{\text{d}}^4}}}{{4{{\text{D}}^3}{\text{n}}}}$$

D

$$\frac{{{\text{C}}{{\text{d}}^4}}}{{8{{\text{D}}^3}{\text{n}}}}$$

When an open coiled helical compression spring is subjected to an axial compressive load, the stress induced in the wire is

A

Tensile stress

B

Compressive stress

C

Shear stress

D

Bending stress

When a close coiled helical spring is compressed, its wire is subjected to

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