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If 10 coils of spring cut out from a spring of 25 coils, then the stiffness of new spring will be
  • a)
    Same as the original spring
  • b)
    1.25 times the original spring
  • c)
    2.5 times the original spring
  • d)
    0.4 times the original spring
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If 10 coils of spring cut out from a spring of 25 coils, then the stif...

⇒k′ = 2.5 k
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If 10 coils of spring cut out from a spring of 25 coils, then the stif...
Answer:

Stiffness of the new spring after cutting 10 coils from a spring of 25 coils can be calculated using the formula:

K = Gd^4/8D^3n

where,
K = stiffness of the spring
G = modulus of rigidity
d = diameter of the wire
D = mean diameter of the spring
n = number of active coils

Given,
Number of coils cut = 10
Original number of coils = 25

Therefore,
Number of active coils in new spring = 25 - 10 = 15

The stiffness of the new spring can be calculated as follows:

K_new = Gd^4/8D^3n_new

K_new = Gd^4/8D^3(15)

Now, we know that the diameter of the wire and the mean diameter of the spring remain constant. Therefore, we can write:

K_new = Kn_old (n_old/n_new)^3

K_new = K_old (25/15)^3

K_new = K_old (1.67)^3

K_new = 2.5 K_old

Therefore, the stiffness of the new spring is 2.5 times the stiffness of the original spring.

Hence, the correct option is (C).
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If 10 coils of spring cut out from a spring of 25 coils, then the stiffness of new spring will bea)Same as the original springb)1.25 times the original springc)2.5 times the original springd)0.4 times the original springCorrect answer is option 'C'. Can you explain this answer?
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