If A=B+(C)/(D+E) ' the dimensions of ' B ' and ' C ' are [L T^-i] and [M^0 L T^0], respectivel

step 1 In this question we have a relation a is equal to b plus c divided by d plus t here dimension of

If A=B+(C)/(D+E) ' the dimensions of ' B ' and ' C ' are [L...

If $A=B+\frac{C}{D+E}$ ' the dimensions of ' $B$ ' and ' $C$ ' are $\left[\mathrm{L} \mathrm{T}^{-\mathrm{i}}\right]$ and $\left[\mathrm{M}^{0} \mathrm{~L} \mathrm{~T}^{0}\right]$, respectively. Find the dimensions of $A, D$ and $E:$ (a) $A=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right], D=[T], E=[\mathrm{LT}]$ (b) $A=\left[\mathrm{MLT}^{0}\right], D=\left[\mathrm{T}^{2}\right], E=\left[\mathrm{T}^{2}\right]$ (c) $A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{MT}], E=[M T]$ (d) $A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{T}], E=[\mathrm{T}]$

If $A=B+\frac{C}{D+E}$ ' the dimensions of ' $B$ ' and ' $C$ ' are $\left[\mathrm{L} \mathrm{T}^{-\mathrm{i}}\right]$ and $\left[\mathrm{M}^{0} \mathrm{~L} \mathrm{~T}^{0}\right]$, respectively. Find the dimensions
of $A, D$ and $E:$
(a) $A=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right], D=[T], E=[\mathrm{LT}]$
(b) $A=\left[\mathrm{MLT}^{0}\right], D=\left[\mathrm{T}^{2}\right], E=\left[\mathrm{T}^{2}\right]$
(c) $A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{MT}], E=[M T]$
(d) $A=\left[\mathrm{LT}^{-1}\right], D=[\mathrm{T}], E=[\mathrm{T}]$

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Key Concepts

Fundamental Dimensions

Fundamental dimensions, such as mass (M), length (L), and time (T), serve as the basic building blocks for expressing the physical dimensions of quantities. They are used to represent a wide range of physical phenomena in a standardized manner.

Dimensional Operations

Dimensional operations involve the rules for multiplying, dividing, and combining dimensions. When dealing with equations involving fractions or products, each term's dimensions must be carefully manipulated according to these rules to maintain overall consistency.

Dimensional Analysis

Dimensional analysis is a technique used to check the consistency of physical equations by ensuring that both sides of an equation have the same fundamental dimensions. This approach helps verify that the mathematical relationships between physical quantities are physically meaningful.

Dimensional Consistency

Dimensional consistency requires that all terms added, subtracted, or equated in an equation must have the same dimensions. This is a fundamental principle in physics that guarantees that the computed results are independent of the units used.

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