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

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

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

An open coiled helical compression spring 'A' of mean diameter 50 mm is subjected to an axial load ‘W’. Another spring 'B' of mean diameter 25 mm is similar to spring 'A' in all respects. The deflection of spring 'B' will be __________ as compared to spring 'A'.

A

One-eighth

B

One-fourth

C

One-half

D

Double

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

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

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

$$4\tau $$

If the spring have same solid length and number of coils in the two springs are 8 and 10, then find the diameter of the spring with 8 coils. It is given diameter of spring with 10 coils is 12mm.

A

9.6mm

B

9mm

C

12mm

D

15mm

A large circular coil of N turns and radius R carries a time varying current $$I = {I_0}\sin \left( {\omega t} \right).$$ A small circular coil of n turns and radius r(r ≪ R) is placed at the centre of the large coil such that the coils are concentric and coplanar. The induced emf in the small coil

A

leads the current in the large coil by $$\frac{\pi }{2}$$

B

lags the current in the large coil by $$\pi $$

C

is in phase with the current in the large coil

D

lags the current in the large coil by $$\frac{\pi }{2}$$

When an open coiled helical compression spring is subjected to an axial load (W), the compression produced in the spring will be (where, n = No. of active turns of the spring and G = Modulus of rigidity for the spring material)

A

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

B

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

C

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

D

$$\frac{{16{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{\text{G}}{{\text{d}}^4}}}$$

Find the mean coil diameter of a helical compression sprig if a load of 1200N is applied on the spring. Spring index is 6, and wire diameter 7mm.

A

7/6mm

B

42mm

C

1200×6/7 mm

D

None of the listed

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

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