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 :
Dimension of Velocity is [L¹T-¹]
❍ Acceleration :
Dimension of acceleration = [L¹ T-²]
❍ Force :
Dimension of Force = [M¹L¹T-²]
❍ Momentum :
Dimension of momentum is [M¹L¹T-¹]
❍ Work :
Dimension of work = [M¹L¹ T-²] [L]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀= [M¹L² T-²]
❍ Power :
Dimension of power = [M¹L² T-³]
❍ Electric Charge :
Dimemsion of Electric Charge = [A¹T¹]
❍ Electric potential :
Dimension of electric potential = [M¹L² T-³A-¹]
❍ Electric resistance :
Dimension of Electric resistance = [M¹L² T-³A-²]
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Answers & Comments
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 :
Dimension of Velocity is [L¹T-¹]
❍ Acceleration :
Dimension of acceleration = [L¹ T-²]
❍ Force :
Dimension of Force = [M¹L¹T-²]
❍ Momentum :
Dimension of momentum is [M¹L¹T-¹]
❍ Work :
Dimension of work = [M¹L¹ T-²] [L]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀= [M¹L² T-²]
❍ Power :
Dimension of power = [M¹L² T-³]
❍ Electric Charge :
Dimemsion of Electric Charge = [A¹T¹]
❍ Electric potential :
Dimension of electric potential = [M¹L² T-³A-¹]
❍ Electric resistance :
Dimension of Electric resistance = [M¹L² T-³A-²]
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