Correct Answer - Option 3 : ML
2T
-3
Concept:
Dimensional Formula
- It depicts the way to relate any unit to fundamental Units.
- If we have to find The dimensional formula of any quantity, At first, we find its units in terms of these fundamental units, and then replace units with these dimensions.
Power
-
The rate of consumption of energy is called power.
P = Δ E / Δt
Δ E = Change in energy, Δt = Change in time
-
Unit of Power: The unit of power is Watt
1 watt = 1 Joule / 1 second
Calculation:
Dimension of Power
\(P = \frac{Dimension\ of \ Energy}{Dimension \ of \ time}\)
Dimension of Energy = Dimension of Work = Dimension of Force × Dimension of displacement
E = [ M L T -2 ] [ L ] = M L 2 T - 2
⇒ P = E / T
\(\implies P = \frac{M L ^{2} T^{-2}}{T} = M L ^{2}T^{-2}T^{-1}\)
⇒ P = M L 2 T (-2 - 1 ) = M L 2 T -3
So, the correct option is ML2T-3
Additional Information:
- Dimensional Formula of Fundamental Units are
Physical Quantity
|
SI Unit
|
Dimension
|
Mass
|
Kg
|
M
|
Time
|
Second
|
T
|
Length
|
Meter
|
L
|
Current
|
Ampere
|
I
|
Temperature
|
Kelvin
|
K
|