# Question #ff50e

Jan 18, 2018

Decreases

#### Explanation:

Suppose, two springs of spring constant $k 1$ and$k 2$ are in series,if we apply force F on both of them and they undergo extension of $x 1$ and $x 2$ then we can write, $F = k 1 x 1$ and $F = k 2 x 2$

Now,suppose these two springs are attached end to end to form a series combination,whose spring constant is $k .$

Now,if we apply same force F we can write,
$F = k x$

now, $x = x 1 + x 2$ (because total extension now will be equal to individuals extension)
or, $\frac{F}{k} = \frac{F}{k 1} + \frac{F}{k 2}$

hence, $\frac{1}{k} = \frac{1}{k 1} + \frac{1}{k 2}$

or,$k = \frac{k 1 k 2}{k 1 + k 2}$