Question

NEET 2017 Q:

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 : -

Answer 1

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