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CBSE Class 11-science Answered

A  spring  of  force constant  K is  cut  into  lengths of  ratio 1:2:3. they  are  connected  into  series and  the  new  force  constant  is  K' . then  they  are  connected in  parallel and  force  constant is K" . Then  K':K"  is ?  
Asked by PARDEEP | 31 Mar, 2018, 03:48: PM
answered-by-expert Expert Answer
Force constant of spring begin mathsize 12px style k space proportional to fraction numerator 1 over denominator l e n g t h end fraction end style
after cutting the spring in the ratio 1:2:3, the force constants will be in the ratio 6:3:2
 
Force constant in series K' is given by : begin mathsize 12px style fraction numerator 1 over denominator K apostrophe end fraction equals space fraction numerator 1 over denominator 6 k end fraction plus fraction numerator 1 over denominator 3 k end fraction plus fraction numerator 1 over denominator 2 k end fraction space equals space 1 over k space semicolon space h e n c e space K apostrophe space equals space k end style
Force constant in parallel K" : 6k+3k+2k = 11k;
 
hence K' / K" = 1 / 11
Answered by Thiyagarajan K | 01 Apr, 2018, 04:05: PM
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