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)
Answers
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)
= [ 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]
❍ Velocity :
- Displacement = [L]
- Time = [T]
Dimension of Velocity is [L¹T-¹]
❍ Acceleration :
- Velocity = [L¹ T-¹]
- Time = [T]
Dimension of acceleration = [L¹ T-²]
❍ Force :
- Mass = [M]
- Acceleration = [L¹ T-²]
Dimension of Force = [M¹L¹T-²]
❍ Momentum :
- Mass = [M]
- velocity = [L¹T-¹]
Dimension of momentum is [M¹L¹T-¹]
❍ Work :
- Force = [M¹L¹ T-²]
- Displacement = [L]
Dimension of work = [M¹L¹ T-²] [L]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀= [M¹L² T-²]
❍ Power :
- Work = [M¹L² T-²]
- Time = [T]
Dimension of power = [M¹L² T-³]
❍ Electric Charge :
- Current = [A]
- Time = [T]
Dimemsion of Electric Charge = [A¹T¹]
❍ Electric potential :
- Work = [M¹L² T-²]
- Charge = [A¹T¹]
Dimension of electric potential = [M¹L² T-³A-¹]
❍ Electric resistance :
- potential difference = [M¹L² T-³A-¹]
- Current = [A]
Dimension of Electric resistance = [M¹L² T-³A-²]
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