Question

A uniform spring of normal length l has a force constant k. It is cut into two pieces of lengths l₁, and l₂ such that l₁ = nl₂ where n is an integer. Then the value of k₁ (force constant of spring of length l₁) is –

• A. $\frac { \mathrm { kn } } { ( \mathrm { n } + 1 ) }$
• B.
• C.
• D. $\frac { \mathrm { kn } } { \mathrm { n } - 1 }$

Answer 1

Answer: (B)

Answer 2

k₁l₁ = k₂l₂ = k(l ₁ + l₂)

k₁ = $\frac { \mathrm { k } \left( \ell _ { 1 } + \ell _ { 2 } \right) } { \ell _ { 1 } }$ or k₁ = $\frac { \mathrm { k } \left( \mathrm { n } \ell _ { 2 } + \ell _ { 2 } \right) } { \mathrm { n } \ell _ { 2 } }$

or k₁ =