Question

If a spring of stiffness '$k$' is cut into two parts '$A$' and '$B$' of length ${\ell }_A={\ell }_B=2:3$, then the stiffness of spring '$A$' is given by:

• A. $\frac{3k}{5}$
• B. $\frac{2k}{5}$
• C. $k$
• D. $\frac{5k}{2}$

Answer 1

The correct option is D $\frac{5k}{2}$

A spring is cut into two parts of length $La$ and $Lb$

Also given that $La:Lb=2:3$

If the length of spring is $L$ , then $La=\frac{2L}{5}$

And length of $B$ , $Lb=\frac{3L}{5}$

We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .

e.g.,$K\alpha \frac{1}{L}$

If intial spring constant is $k$ then,

$kL=KaLa=KbLb$

Then,$Ka=\frac{k}{\left(2/5\right)}=\frac{5k}{2}$

And $Kb=\frac{k}{\left(3l/5\right)}=\frac{5k}{3}$

Hence, stiffness of $A$ is given by $\frac{5k}{2}$

Therefore the correct option is D