A spring of natural length $L$ has spring constant $k$. If it is cut into two pieces of lengths in ratio $1:2$, the spring constants of the two pieces are:
A$k$ and $2k$
B$3k$ and $3k/2$
C$k/3$ and $2k/3$
D$2k$ and $k$
Answer & Solution
Correct answer: B. $3k$ and $3k/2$
$k \propto 1/L$. Pieces are $L/3$ and $2L/3$. Constants: $k \cdot (L/(L/3)) = 3k$ and $k \cdot (L/(2L/3)) = 3k/2$. (Shorter piece is stiffer.)
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