Question

A spring of length 3L & spring constant k is cut into 2 parts of length L & 2L what is the ratio of spring constant of two parts?​

Answer 1

Given:

A spring of length 3L & spring constant k is cut into 2 parts of length L & 2L.

To find:

Ratio of spring constant of two parts?

Calculation:

When spring is cut , the product of the spring constant and length remains constant:

Let spring constant of L segment be k_(1):

$\therefore \: 3L \times k = L \times k_{1}$

$\implies\: k_{1} = 3k$

Let spring constant of L segment be k_(2):

$\therefore \: 3L \times k =2 L \times k_{2}$

$\implies\: k_{2} = \dfrac{3k}{2}$

Now the ratio:

$\therefore \: k_{1} : k_{2} = 3k : \dfrac{3k}{2}$

$\implies\: k_{1} : k_{2} = 3 : \dfrac{3}{2}$

$\implies\: k_{1} : k_{2} = 1 : \dfrac{1}{2}$

$\implies\: k_{1} : k_{2} = 2 : 1$

So, the ratio is 2:1 .