Q.

A spring of force constant k is cut into length of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'.Then they are connected in parallel and force constant is k''. Then k' : k'' is :

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a

1 : 11

b

1 : 9

c

1 : 14

d

1 : 16

answer is B.

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Detailed Solution

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As we know spring constant k  1l

Length of the spring segments = l6, l3, l2

So spring constants for spring segments will be k1 = 6k, k2 = 3k, k3 = 2k

So in parallel combination,

k'' = k1+k2+k3 = 11k

In series combination, 1k' = 16k+13k+12k=1+2+36k=1k

Hence k' : k'' = 1 : 11

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