Question

Spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and their new force constant is k’. Then they are connected in parallel then their force constant is k”. Then k’ : k” is

Answer 1

The ratio of K' and K'' is 1 : 11.

Spring of force constant K is cut into length of ratio 1 : 2 : 3. They are connected in series and their new force constant is K'. and then they are connected in parallel then their force constant is K''.

We have to find the ratio of K' and K''.

We know from Hook's law, F = -kx.

If force is constant then, spring constant is inversely proportional to the length of spring.

∴ the ratio of spring constant of pieces of spring = 1/1 : 1/2 : 1/3 = 6 : 3 : 2

Let the proportionality constant is κ.

Spring constants are ; 6κ , 3κ , 2κ

Case 1 : when these springs are joined in series combination.

$\frac{1}{K_{eq}}=\frac{1}{K_1}+\frac{1}{K_2}+\frac{1}{K_3}\\\\=\frac{1}{6k}+\frac{1}{3k}+\frac{1}{2k}\\\\=\frac{6}{6k}=\frac{1}{k}\\\\\implies K'=k$

Case 2 : when these springs are connected in parallel combination.

$K_{eq}=K"=K_1+K_2+K_3=6k+3k+2k=11k$

∴ the ratio of K' and K'' is k/11k = 1 : 11.

Also read similar questions : three spring of spring constant K are connected in series and parallel with the mass M calculate the ratio of frequency ...

https://brainly.in/question/15754435

An object is falling freely under the gravitational force. Its velocity after traversing a distance h is v. If v depends...

https://brainly.in/question/11911767

Answer 2

Answer:from which book is this question from

Explanation: