Question

A spring of force constant $k$ is cut out into two pieces whose lengths are in the ratio $1:2.$ What is the force constant of the longer piece

• A. $\frac{k}{2}$
• B. $1.5K$
• C. $2k$
• D. $3k$

Answer 1

The correct option is B $1.5K$

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$=K^1$

Force constant $\alpha$ $1/L$ length of the spring

$K/K^1=\left(2L/3\right)L$

$K/K^1=2/3$

$K^1=3K/2$

$K^1=1.5K$

Force constant of larger piece is $1.5K.$

Hence,

option $\left(B\right)$ is correct answer.