question_answer

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of [IIT-JEE (Screening) 1999]

A)            \[(2/3)k\]                              

B)            \[(3/2)k\]

C)            \[3k\]                                      

D)            \[6k\]

Correct Answer: B

Solution :

                                 Force constant \[(k)\propto \frac{1}{\text{Length}\,\text{of}\,\text{spring}}\]                    \[\Rightarrow \] \[\frac{K}{{{K}_{1}}}=\frac{{{l}_{1}}}{l}=\frac{\frac{2}{3}l}{l}\] \[\Rightarrow \] \[{{K}_{1}}-\frac{3}{2}K\].