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

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

Bissoy MCQ
#Mechanical Engineering #Strength Of Materials In ME

Related Questions

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
The stiffness of a closely coiled helical spring subjected to an axial load W is equal to (where G = Modulus of rigidity and n = Number of active coils)
A $$\frac{{{\text{G}}{{\text{d}}^4}}}{{8{{\text{D}}^3}{\text{n}}}}$$
B $$\frac{{{\text{G}}{{\text{d}}^3}}}{{8{{\text{D}}^3}{\text{n}}}}$$
C $$\frac{{{\text{G}}{{\text{d}}^4}}}{{4{{\text{D}}^3}{\text{n}}}}$$
D $$\frac{{{\text{G}}{{\text{d}}^4}}}{{8{{\text{D}}^2}{\text{n}}}}$$
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 $$4\tau $$
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 $$\frac{{{\text{C}}{{\text{d}}^4}}}{{8{{\text{D}}^3}{\text{n}}}}$$
A close coil helical spring of mean diameter D consists of n coils of diameter d. If it carries an axial load W, the energy stored in the spring, is
A $$\frac{{4{\text{W}}{{\text{D}}^2}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$
B $$\frac{{4{{\text{W}}^2}{\text{Dn}}}}{{{{\text{d}}^4}{\text{N}}}}$$
C $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$
D $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{{\text{n}}^2}}}{{{{\text{d}}^4}{\text{N}}}}$$
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
If the modulus of elasticity for a given material is twice its modulus of rigidity, then bulk modulus is equal to
A 2C
B 3C
C $$\frac{{2{\text{C}}}}{3}$$
D $$\frac{{3{\text{C}}}}{2}$$
Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?
A E = 2G (1 + v)
B E = G (1 + v)
C $${\text{E}} = \frac{{{\text{G}}\left( {1 + {\text{v}}} \right)}}{2}$$
D E = 2G (1 + 2v)
One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where $$\delta $$ = Deflection of the spring.)
A $$2\pi \sqrt {\frac{g}{\delta }} $$
B $$\frac{1}{{2\pi }}\sqrt {\frac{g}{\delta }} $$
C $$2\pi \sqrt {\frac{\delta }{g}} $$
D $$\frac{1}{{2\pi }}\sqrt {\frac{\delta }{g}} $$

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