If a spring of stiffness $k$ is cut into two parts $A$ and $B$ of length $l_{A}: l_{B}=2: 3$, then the stiffness of spring $A$ is given by
AIEEE 2011, Medium
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$k \propto \frac{1}{\ell}$
$\frac{ k _{ A }}{ k } =\frac{1}{ l _{ A }}$
$k _{ A } =\frac{ l _{ A }+ l _{ B }}{ l _{ A }} \cdot k$
$k _{ A }=\frac{\frac{ l _{ A }}{ l _{ B }}+1}{\frac{ l _{ A }}{ l _{ B }}} \cdot k$
$k _{ A }=\frac{\frac{2}{3}+1}{\frac{2}{3}} \cdot k$
$k _{ A }=\frac{5}{2} \cdot k$
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