# Two springs are connected in series and the combination is pulled by a constant force. If spring constant of two springs are $ $K\text{ and 2}K$ , then the ratio of potential energy stored in the springs is

Answer

Verified

178.2k+ views

**Hint**We know that PE is the amount of energy started at the highest point.

Here, two springs are converted in series

Therefore, using $P.E=\dfrac{1}{2}{{K}_{2}}$

**Complete Step by Step Solution**

$2:1$

For spring ${{S}_{1}}\text{ the spring constant is }K$

For spring${{S}_{2}}$ the spring constant is $2K$

Now, applying the potential energy formula for spring ${{S}_{1}}$

i.e. $P{{E}_{1}}=\dfrac{1}{2}K{{r}^{2}}$ …… (1)

Similarly, we use the above formula for spring ${{S}_{2}}$

i.e.$P{{E}_{2}}=\dfrac{1}{2}2K\text{ }{{x}^{2}}$ …… (2)

Now, dividing equation (2) by equation (1)

We get $\dfrac{P{{E}_{2}}}{P{{E}_{1}}}=\dfrac{1}{2}K{{x}^{2}}\times \dfrac{2}{\left( 2K \right){{x}^{2}}}$

Now, cancelling all the common factors in the above equation we get

$\dfrac{P{{E}_{2}}}{P{{E}_{1}}}=\dfrac{1}{2}$

Or for simplicity we can write this as also

$\dfrac{P{{E}_{2}}}{P{{E}_{1}}}=\dfrac{1}{2}$

**Therefore, the ratio of the two potential angles is $2:1$**

**Note**Above discussion of Potential Energy that is stored in the spring can be found out using $\dfrac{1}{2}k{{x}^{2}}$formula in which$k=\text{Spring Constant}$.

In this case, we reciprocate this energy with respect to the other.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main