When a helical compression spring is cut into halves, the stiffness of the resulting spring will be

A closely-coiled helical spring is cut into two halves. The stiffness of the resulting spring will be

A

Same

B

Double

C

Half

D

One-fourth

A helical coil spring of stiffness k is cut to two equal halves and then these are connected in parallel to support a vibrating mass m. The angular frequency of vibration, ωn is

A

√k/m

B

√2k/m

C

√4k/m

D

√k/4m

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

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

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

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 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

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

A potato tuber has been cut into two halves. A few drops of iodine solution are placed on the cut surface of one of the halves. What colour change will be noticed?

A

From brown to blue-black

B

From brown to orange-red

C

From blue to pink

D

From pink to blue-green

A long helical spring having a spring stiffness of 12 kN/m and number of turns 20, breaks into two parts with number of turns 10 each in both the parts. If the two parts are connected in series, then the softness of the resultant spring will be

A

6 kN/m

B

12 kN/m

C

24 kN/m

D

30 kN/m

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?

A

8

B

9

C

11

D

12

When a helical compression spring is cut into halves, the stiffness of the resulting spring will be

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