Question

Find the dimensions of
1. Velocity
2. acceleration
3. Force
4. Momentum
5. Work
6. Power
7. Electric charge
8. Electric potential
9. Electric resistance
10. Capacitance (C)​

Answer 1

Dimensions of

1. Velocity

Velocity = displacement/time

              = L / T

              = [M° L¹ T⁻¹]

2.Acceleration

Acceleration = (change in velocity)/(change in time)

                     = (m/s)/(s) = (m)/(s * s)

                     = L / T²

                     = [M° L¹ T⁻²]

3. Force

Force = mass * acceleration

          = kg * m/s²

          = [M¹ L¹ T⁻²]

4. Momentum

Momentum = mass * velocity

                   = M * (L / T)

                   = [M¹ L¹ T⁻¹]

5. Work

Work = Force * displacement

         = [M¹ L¹ T⁻²] * [L¹]

         = [M¹ L² T⁻²]

6. Power

Power = work/time

           = [M¹ L² T⁻²] / [ T¹ ]

           = [M¹ L² T⁻³]

7.Electric charge

Electric charge (Q) = It

                               =  A * T

                               =  [ M° L° A¹ T¹ ]

8. Electric potential

Electric potential = W/Q = (work done)/(per unit charge)

                          = [M¹ L² T⁻²] / [ A¹ T¹ ]

                          = [ M¹ L² A⁻¹ T⁻³ ]

9. Electric resistance

Electric resistance = (change in potential)/(current)

So,                        R = (ΔV)/(I)

$\boxed{\bf{\therefore V = IR}}$

                       = [ M¹ L² A⁻¹ T⁻³ ] / [ A¹ T¹ ]

                       = [ M¹ L² A⁻² T⁻⁴ ]

10. Capacitance (C)

Q = CV     [Q = charge, and V = potential]

So,

C = Q/V

  = [ AT ] / [M¹ L² A⁻¹ T⁻³]

  = [M⁻¹ L⁻² A² T⁴]

Answer 2

$\large \underline{\sf{Answer :}} \\ \\ \sf\dag{\purple{\underline{Dimensions \: of \: the \: Following : }}}$

❍ Velocity :

$\bullet \: \sf \: Formula = \frac{Displacement}{time}$

• Displacement = [L]
• Time = [T]

Dimension of Velocity is [L¹T-¹]

❍ Acceleration :

$\bullet \: \sf \: Formula = \frac{v - u}{t}$

• Velocity = [L¹ T-¹]
• Time = [T]

Dimension of acceleration = [L¹ T-²]

❍ Force :

$\bullet \: \sf \: Formula = mass\times{acceleration}$

• Mass = [M]
• Acceleration = [L¹ T-²]

Dimension of Force = [M¹L¹T-²]

❍ Momentum :

$\bullet \: \sf \: Formula = mass\times{velocity}$

• Mass = [M]
• velocity = [L¹T-¹]

Dimension of momentum is [M¹L¹T-¹]

❍ Work :

$\bullet \: \sf \: Formula = Force\times{Displacement}$

• Force = [M¹L¹ T-²]
• Displacement = [L]

Dimension of work = [M¹L¹ T-²] [L]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀= [M¹L² T-²]

❍ Power :

$\bullet \: \sf \: Formula = \frac{Work}{Time}$

• Work = [M¹L² T-²]
• Time = [T]

Dimension of power = [M¹L² T-³]

❍ Electric Charge :

$\bullet \: \sf \: Formula = Current\times{Time}$

• Current = [A]
• Time = [T]

Dimemsion of Electric Charge = [A¹T¹]

❍ Electric potential :

$\bullet \: \sf \: Formula =\frac{work\:done}{charge}$

• Work = [M¹L² T-²]
• Charge = [A¹T¹]

Dimension of electric potential = [M¹L² T-³A-¹]

❍ Electric resistance :

$\bullet \: \sf \: Formula = \frac{Potential\: Difference}{Current}$

• potential difference = [M¹L² T-³A-¹]
• Current = [A]

Dimension of Electric resistance = [M¹L² T-³A-²]

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