Question

A uniform spring has an unstreched length l and a force constant k. The spring is cut into two parts of unstreched length l₁ and l₂ such that l₁ = hl₂ where h is an integer. The corresponding force constants k₁ and k₂ are :

• A. kh and k(h + 1)
• B. $\frac { k ( \eta + 1 ) } { \eta }$ and k(h – 1)
• C. $\frac { k ( \eta - 1 ) } { \eta }$and k(h+1)
• D. $\frac { k ( \eta + 1 ) } { \eta }$and k(h+1)

Answer 1

Answer: (D)

$\frac { k ( \eta + 1 ) } { \eta }$and k(h+1)

Answer 2

l₁ = h l₂ ̃ l₁ : l₂ = h : 1

̃ l₁ = $\frac { \eta } { \eta + 1 }$ l & l₂ = $\frac { 1 } { ( \eta + 1 ) }$ l

so k₁ = $\frac { \eta + 1 } { \eta }$ k, k₂ = (h + 1) k