Mechanical Engineering Exam  >  Mechanical Engineering Questions  >  A length of 10 mm diameter steel wire is coil... Start Learning for Free
A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will be

  • a) 
    K
  • b) 
    1.25 K
  • c) 
    1.56 K
  • d) 
    1.96 k
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A length of 10 mm diameter steel wire is coiled to a close coiled heli...
Given:
Diameter of steel wire = 10 mm
Number of coils (n1) = 8
Mean diameter (D1) = 75 mm

To find:
Spring stiffness (K1)

Formula used:
The spring stiffness can be calculated using the following formula:
K = Gd⁴/ 8D³n
where,
K = Spring stiffness
G = Modulus of rigidity of the material
d = Diameter of the wire
D = Mean diameter of the spring
n = Number of coils

Calculation:

Given,
d = 10 mm
n1 = 8
D1 = 75 mm

To find K1, we need to calculate G first. The modulus of rigidity (G) for steel is 80 GPa.
Therefore,
G = 80 GPa = 80 x 10^3 MPa

Now, we can calculate the spring stiffness K1 using the formula mentioned above:
K1 = (80 x 10^3 x 10^(-6) x 10^4)/(8 x 75^3 x 8) = 4.48 N/mm

Next, we need to find the spring stiffness when the same length of wire is coiled to 10 coils of mean diameter 60 mm. Let us assume the stiffness of this new spring to be K2.

Given,
n2 = 10
D2 = 60 mm

Using the same formula mentioned above, we can calculate K2 as follows:
K2 = (80 x 10^3 x 10^(-6) x 10^4)/(8 x 60^3 x 10) = 7.008 N/mm

Therefore, the spring stiffness when the same length of wire is coiled to 10 coils of mean diameter 60 mm is 7.008 N/mm.

Answer:
The correct option is (c) 1.56 K.
Free Test
Community Answer
A length of 10 mm diameter steel wire is coiled to a close coiled heli...
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer?
Question Description
A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A length of 10 mm diameter steel wire is coiled to a close coiled helical spring having 8 coils of 75 mm mean diameter, and the spring has a stiffness K. If the same length of wire is coiled to 10 coils of 60 mm mean diameter, then the spring stiffness will bea)Kb)1.25 Kc)1.56 Kd)1.96 kCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
Explore Courses for Mechanical Engineering exam

Top Courses for Mechanical Engineering

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev