Question

Write the relationship or formula , Dimensions and Dimensional formula of the given quantities
1.Area
2. Volume
3. Mass density
4. Frequency
5. Velocity
6. Acceleration
7. Force
8. Impulse
9. Work
10. Power​

Answer 1

$\bold{1.Area} \\ \bold{Formula} - Length \times Breadth \\ \bold{Dimension} - [ {L}^{2} ] \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{2} {T}^{0} ]\\</p><p> ----------------\\\bold{2.Volume} \\ \bold{Formula} - Length \times Breadth \times Height \\ \bold{Dimension} - [ {L}^{3} ] \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{3} {T}^{0} ]\\---------------------- \\ \bold{3.Mass \: Density} \\ \bold{Formula} - \frac{Mass }{Volume} \\ \bold{Dimension} - \frac{[M]}{ [ {L}^{3} ]} \\ \bold{Dimensional \: Formula} - [ {M}^{1} {L}^{ - 3} {T}^{0} ]\\ ----------------------\\ \bold{4.Frequency} \\ \bold{Formula} - \frac{1}{Time \: Period} \\ \bold{Dimension} - \frac{1}{[T]} \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{0} {T}^{ - 1} ]\\ -------------------\\ \bold{5.Velocity} \\ \bold{Formula} - \frac{Displcement}{Time} \\ \bold{Dimension} - \frac{[L]}{[T]} \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{0} {T}^{ - 1} ]\\---------------------- \\ \bold{6.Accleration} \\ \bold{Formula} - \frac{Velocity}{Time} \\ \bold{Dimension} - \frac{[l {t}^{ - 1} ]}{[t]} \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{0} {T}^{ - 2} ]\\ --------------------\\ \bold{7.Force} \\ \bold{Formula} - Mass \times Accleration \\ \bold{Dimension} - [ML {T}^{ - 2} ] \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{0} {T}^{ - 2} ]\\ ----------------\\ \bold{8.Impulse} \\ \bold{Formula} - Force \times Time \\ \bold{Dimension} - [MLT][T] \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{1} {T}^{-1} ]\\-----------------$

$\bold{9.Power} \\ \bold{Formula} - \frac{Work}{Time} \\ \bold{Dimension} - \frac{[M {L}^{ 2} {T}^{ - 2} }]{[T]} \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{2} {T}^{ - 3} ]\\------------------- \\ \bold{10.Momentum} \\ \bold{Formula} - Mass \times Velocity \\ \bold{Dimension} - [M][L {T}^{ - 1} ] \\ \bold{Dimensional \: Formula} - [ {M}^{0} {L}^{2} {T}^{0}$

Answer 2

$\huge\textbf{Answer}$

(1).Area

• Forumla is (L × B) Length × Breadth
• L² is the dimensions
• (M°L²T°) is the dimensional Formula

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(2).Volume

• Formula is (L × B × H) Length × Breadth × Height)
• L³ is the dimensions
• M°L³1°is the dimensional Formula

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(3).Mass density

• Formula is M/V
• M/L³ is the dimensions
• M¹L-³T° is the dimensional Formula

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(4).Frequency

• Formula is 1/Time
• 1/T is the dimensions
• M°L°T-¹ is the dimensions formula

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(5).Velocity

• Formula is Displacement / T
• L/T is the Dimensions
• M°L°T-¹ is the dimensional Formula

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(6).Acceleration

• Formula is V/T
• IT-¹/T is the dimensions
• M°L°t-² is the Dimensional Formula

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(7).Force

• Formula is -M × Acceleration
• LT -2 is the dimensions
• M°L°T-² is the dimensions Formula

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(8).Impulse

• Formula is F×T
• MLT°T Is the dimensions
• M°T¹T-¹ so the dimensions formul

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(9). Work

• Formula is W/T
• ML²T²(C) is the dimensions
• M°L²T-³ is the dimensional Formula

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(10). Power

• Formula is M × V
• (M) (LT-¹) is the dimensions
• M°L²T° is the dimensions formula

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