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Oscillations

Question
CBSEENPH11020821

A spring of force constant k is cut into lengths 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

  • 1:6

  • 1:9

  • 1:11

  • 1:14

Solution

C.

1:11

Sping space constant space proportional to space 1 over length
straight k proportional to space 1 over straight l
straight i. straight e. space straight k subscript 1 space equals space 6 straight k
straight k subscript 2 space equals space 3 straight k
straight k subscript 3 space equals space 2 straight k
In space series space
fraction numerator 1 over denominator straight k apostrophe end fraction space equals space fraction numerator 1 over denominator 6 straight k end fraction space plus space fraction numerator 1 over denominator 3 straight k end fraction space plus space fraction numerator 1 over denominator 2 straight k end fraction
fraction numerator 1 over denominator straight k apostrophe end fraction space equals space fraction numerator 6 over denominator 6 straight k end fraction
straight k apostrophe space equals space straight k
straight k apostrophe apostrophe space equals space 6 straight k space plus space 3 straight k plus space 2 straight k
straight k apostrophe apostrophe space equals space 11 straight k
fraction numerator straight k apostrophe over denominator straight k apostrophe apostrophe end fraction space equals 1 over 11
1 colon 11