Question

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

• A. 2 k/3
• B. 3 k/2
• C. 3 k
• D. 6 k

Answer 1

The correct option is B 3 k/2

Length of the spring $=L$

Force constant of spring $=K$

Ratio in which spring is cut $=1:2$

Length of larger piece $=2L/(2+1)=2L/3$

Force constant of larger piece $=K^{\prime }$

Force constant ∝ 1 / Length of the spring

$K/K^{\prime }=\left(2L/3\right)/L$

$K/K^{\prime }=2/3$

$K^{\prime }=3K/2$

$K^{\prime }=1.5K$

Force constant of larger piece is $1.5K$