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Two close-coiled springs are subjected to the same axial force. If the second spring has four times the coil diameter, double the wire diameter and double the number of coils of the first spring, then the ratio of deflection of the second spring to that of the first will be: 
  • a)
    8
  • b)
    2
  • c)
    1/2
  • d)
    1/16
Correct answer is option 'A'. Can you explain this answer?
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Solution:

Given: Two close-coiled springs are subjected to the same axial force.

Let's consider the following data:

First Spring:

- Coil Diameter = D
- Wire Diameter = d
- Number of Coils = N

Second Spring:

- Coil Diameter = 4D (four times the coil diameter of the first spring)
- Wire Diameter = 2d (double the wire diameter of the first spring)
- Number of Coils = 2N (double the number of coils of the first spring)

Now, we need to find the ratio of deflection of the second spring to that of the first spring.

Deflection of a spring is given by:

𝛿 = (F * L) / (G * d^4 * N)

where 𝛿 is deflection, F is axial force, L is length, G is modulus of rigidity, d is wire diameter, and N is number of coils.

As both springs are subjected to the same axial force, we can ignore the force term in the above equation.

Length of the first spring, L1 = D*N*d

Length of the second spring, L2 = 4D*2N*2d = 16DNd

The ratio of deflection of the second spring to that of the first spring can be given as:

𝛿2 / 𝛿1 = (L2 / L1) * (d1 / d2)^4 * (N1 / N2)

Substituting the given values, we get:

𝛿2 / 𝛿1 = (16DNd / DNd) * (d / 2d)^4 * (N / 2N)

Simplifying the above equation, we get:

𝛿2 / 𝛿1 = 8

Therefore, the ratio of deflection of the second spring to that of the first spring is 8.

Thus, the correct answer is option A.
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Two close-coiled springs are subjected to the same axial force. If the second spring has four times the coil diameter, double the wire diameter and double the number of coils of the first spring, then the ratio of deflection of the second spring to that of the first will be:a)8b)2c)1/2d)1/16Correct answer is option 'A'. Can you explain this answer?
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