Question

define dimensions and dimensional formula?

Answer 1

DIMENSIONS are the powers to which the fundamental quantities are raised to represent other physical quantities.

DIMENSIONAL FORMULA is an expression in which dimensions of a physical quantity is represented in terms of fundamental quantities.

Answer 2

$\textbf{DIMENSIONS}$

→ The dimension of a physical quantity are the power to which the units of the base quantities are raised to represent a derived unit of that quantity.

→ Units which are in brackets are known as Derived formula.
Ex :- [M¹L¹T-²]

→ Units which are in brackets with equal signs are known as Derived equation.
Ex :- Force = [M¹L¹T-²]

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$\textbf{Dimensional Formula}$

$\underline{Height}$

= [L¹]

$\underline{Area}$

= [L²]

$\underline{Volume}$

= [L³]

$\underline{Density}$

= Mass/Volume

= [M¹L-³]

$\underline{Speed}$

= Distance/Time

= [L¹T-¹]

» Dimensions of Speed and Velocity are same

$\underline{Acceleration}$

= Velocity/Time

= [L¹T-²]

$\underline{Force}$

= Mass × Acceleration

= [M¹L¹T-²]

» Dimensions of Force and Thrust are same.

$\underline{Potential Energy}$

= mgh

= [M¹L²T-²]

» Dimensions of Kinetic energy, Potential energy, Tor

$\underline{Pressure}$

= Thrust/Area

= [M¹L-¹T-²]

$\underline{Work Done}$

= force × displacement

= [M¹L-¹T-²]

$\underline{Universal Constant Of Gravitation}$

G = [(Fr²) ÷ (m1m2)]

= [M-¹L³T-²]

$\underline{Power}$

= Work done/Time

= [M¹L²T-²]

» Dimensions of Work done and Energy density are same.

* Energy density = Energy/Volume

$\underline{Impulse}$

= force × time

= [M¹L¹T-¹]

$\underline{Electric Charge}$

= It (Here I is current)

= [A¹T¹]

$\underline{Electric Potential}$

= Work done/Charge

= [M¹L²T-³A-¹]

$\underline{Electric Resistance}$

= Potential difference/Current

= [M¹L²T-³A-²]

$\underline{Planck's Constant}$

= Energy/Frequency

= [M¹L²T-¹]

» Dimensions of Planck's constant and Angular Momentum are same

* Frequency = [T-¹]

$\underline{Electric Capacitance}$

= Charge/Potential

= [M-¹L-²T⁴A²]

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