# The effective spring constant of two spring system as shown in figure will be  Option 1) K1 + K2 Option 2) $\frac{K_{1}K_{2}}{K_{1} + K_{2}}$ Option 3) K1 - K2 Option 4) $\frac{K_{1}K_{2}}{K_{1} - K_{2}}$

V Vakul

When external force is appiled, one spring gets extended and another one gets contracted by same distance. Hence, due to two springs act in same same direction. i. e.

$F = F_{1} + F_{2} \Rightarrow -kx = k_{1}x - k_{2}x \Rightarrow k = k_{1} + k_{2}$

Series combination of spring -

- wherein

$\frac{1}{K_{eq}}= \frac{1}{K_{1}}+ \frac{1}{K_{2}}$

$K_{1}and\ K_{2}$ are spring constants of spring 1 & 2 respectively.

Option 1)

K+ K2

This is correct.

Option 2)

$\frac{K_{1}K_{2}}{K_{1} + K_{2}}$

This is incorrect.

Option 3)

K- K2

This is incorrect.

Option 4)

$\frac{K_{1}K_{2}}{K_{1} - K_{2}}$

This is incorrect.

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