Answer
64.8k+ views
Hint: Formula for frequency is:
$\dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{LC}}} $ (L is the inductor, C is the capacitor)
As per electrical and mechanical analogy conversion, in force current analogy M is the capacitor (C) and k is the reciprocal of the inductor (1/L).
Let’s find the value of k using series and parallel connections (using 1/L = k, in series connections are added with their direct connections and the parallel connection have reciprocal addition).
Complete step by step solution:
As we are provided with an inductor and capacitor in the system then we will add the reciprocal of the inductor for the series connection.
$K = {K_1} + {K_2}$
First, we will do the calculation for series connection:
$
\Rightarrow {K_1} = \dfrac{1}{{2k}} + \dfrac{1}{{2k}} \\
\Rightarrow {K_1} = \dfrac{{2k \times 2k}}{{2k + 2k}}
$ (Taking LCM)
$ \Rightarrow {K_1} = \dfrac{{2k}}{{2k}} = 1k$
Now, we will calculate for the springs in parallel:
$
\Rightarrow {K_2} = \dfrac{1}{{\dfrac{1}{{2k}}}} + \dfrac{1}{{\dfrac{1}{k}}} \\
\Rightarrow {K_2} = 2k + k = 3k$ (in parallel connection we have to take the reciprocal of the spring constants)
Total value of K comes out to be:
$
\Rightarrow K = {K_1} + {K_2} \\
\Rightarrow K = k + 3k = 4k $
From the equation of frequency:
$
\Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{M\dfrac{1}{K}}}} \\
\Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{K}{M}} $ (We have substituted the value of LC as per formula of frequency)
$ \Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{{4k}}{M}} $ (We have substituted the values M and K).
Hence, Option B is correct.
Note: In the question above we have used electrical to mechanical equivalent system of force current, where current is acting as the force in a mechanical system, mass as capacitor, frictional coefficient as reciprocal of R resistor, spring constant as reciprocal of L inductor, displacement as magnetic flux and velocity as voltage.
$\dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{LC}}} $ (L is the inductor, C is the capacitor)
As per electrical and mechanical analogy conversion, in force current analogy M is the capacitor (C) and k is the reciprocal of the inductor (1/L).
Let’s find the value of k using series and parallel connections (using 1/L = k, in series connections are added with their direct connections and the parallel connection have reciprocal addition).
Complete step by step solution:
As we are provided with an inductor and capacitor in the system then we will add the reciprocal of the inductor for the series connection.
$K = {K_1} + {K_2}$
First, we will do the calculation for series connection:
$
\Rightarrow {K_1} = \dfrac{1}{{2k}} + \dfrac{1}{{2k}} \\
\Rightarrow {K_1} = \dfrac{{2k \times 2k}}{{2k + 2k}}
$ (Taking LCM)
$ \Rightarrow {K_1} = \dfrac{{2k}}{{2k}} = 1k$
Now, we will calculate for the springs in parallel:
$
\Rightarrow {K_2} = \dfrac{1}{{\dfrac{1}{{2k}}}} + \dfrac{1}{{\dfrac{1}{k}}} \\
\Rightarrow {K_2} = 2k + k = 3k$ (in parallel connection we have to take the reciprocal of the spring constants)
Total value of K comes out to be:
$
\Rightarrow K = {K_1} + {K_2} \\
\Rightarrow K = k + 3k = 4k $
From the equation of frequency:
$
\Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{M\dfrac{1}{K}}}} \\
\Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{K}{M}} $ (We have substituted the value of LC as per formula of frequency)
$ \Rightarrow f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{{4k}}{M}} $ (We have substituted the values M and K).
Hence, Option B is correct.
Note: In the question above we have used electrical to mechanical equivalent system of force current, where current is acting as the force in a mechanical system, mass as capacitor, frictional coefficient as reciprocal of R resistor, spring constant as reciprocal of L inductor, displacement as magnetic flux and velocity as voltage.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)