Question

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

Answer 1

According to Hooke's elasticity theory for springs :-

Spring constant * Length = constant.

Let us consider that the length of the spring is m units.

Therefore, m*k = constant.

Let us spring constant of longer and shorter length be k1 and k2 respectively.

So,

Longer length will be two-third of the whole length of the spring.

That is, length of the longer length will be 2m/3.

Therefore,

m*k = 2m/3*k1 = constant

Thus simplifying we get,

k1 = 3k/2

HENCE, SPRING CONSTANT OF LONGER PIECE WILL BE 3k/2.