Question

Find the dimensional formula of length assuming force,energy and velocity to be fundamental quatities.
.plzz answer fast​

Answer 1

Answer:

Let's assume that length can be dimensionally represented in the form of energy, force and Velocity as follows :

$L = {F}^{a} \: {E}^{b} \: {V}^{c}$

we just need to do that value of a , b , c :

Now simplifying each of the force , energy and velocity terms , we get :

$= > L = {(ML {T}^{ - 1} )}^{a} \: {(M {L}^{2} {T}^{-1}) }^{b} \: {(L {T}^{-1}) }^{c}$

$= > L = {M}^{(a +b)} {L}^{(a + 2b + c)} {T}^{( - 2a - 2b - c)}$

Comparing terms on each side and Making equations :

$a + b = 0 \: .......(1)$

$a + 2b + c = 1 \: .....(2)$

$- 2b - 2c - c = 0 \: .....(3)$

Solving each equations , we get :

$\boxed{ \bold{a = - 1, \: b = 1, \: c = 0}}$

So final answer :

$\boxed{ \boxed{ \red{ \huge{ \bold{ \{L \} = \{{F}^{ - 1} \: {E}^{1} \: {V}^{0} \}}}}}}$

Answer 2

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QUESTION :

Find the dimensional formula of length assuming force,energy and velocity to be fundamental quatities.

Find the dimensional formula of length assuming force,energy and velocity to be fundamental quatities..plzz answer fast..

CONCEPT USED :

Principle of Homogeneity.

SOLUTION :

In this question, we have to assume force,energy and velocity to be fundamental quatities.

Let Force be represented as F

Let velocity be represented as V

Let Energy be represented as E

According to the principle of Homogeneity :

$L =k { F } ^ { a } \times { V } ^ { b } \times { E } ^ { c }$

$F = { M } ^ { 1 } { L } ^ { 1 } { T } ^ { -2 }$

$V = { M } ^ { 0 } { L } ^ { 1 } { T } ^ { -2 }$

$E = { M } ^ { 1 } { L } ^ { 2 } { T } ^ { -2 }$

So ,

$L =k { { M } ^ { 1 } { L } ^ { 1 } { T } ^ { -2 } } ^ { a } \times { { M } ^ { 0 } { L } ^ { 1 } { T } ^ { -2 } } ^ { b } \times { { M } ^ { 1 } { L } ^ { 2 } { T } ^ { -2 } } ^ { c }$

$=> { M } ^ { 0 } \times { L } ^ 1 \times { T } ^ { 0 } = k \times { M } ^ { a + b } \times { L } ^ { a +b+2c } \times { T } ^{ -2b-2c }$

$Comparing \: The \: Coefficients \::-$

$a + b = 0 \\ \\ a + b + 2c = 1 \\ \\ -2b - c = 0$

=> a = -b = - 1 / 2

Hence, 2c = 1 => c = { 1 / 2 }

-2b - 2c = 0

=> b = 1 / 2

So the final answer is :

$L = { F } ^ {1} { E } ^ { -1 } { V } ^ { 0 } \: Or \: \\ \\ {\sf{\boxed{\blue{L = \dfrac{ F } { E }}}}}$