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 :

Options

A. `(2)/(3)k`
B. `(3)/(2)k`
C. `3k`
D. `6k`

Answer

D

Explanation

Since, `kprop(1)/(l) therefore (k_(1))/(k_(2))=(l_(2))/(l_(1))` But `l_(1)=2l_(2)` (Given)
`therefore (k_(1))/(k_(2))=(l_(2))/(2l_(1))=(1)/(2)ork_(1)=(k_(2))/(2)`
As series combination of both cutting portions gives original spring, `(1)/(k)=(1)/(k_(1))+(1)/(k_(2))=(2)/(k_(2))+(1)/(k_(2))=(3)/(k_(2))`
or `k_(2)=3k therefore k_(1)=(k_(2))/(2)=(3)/(2)k`