The dimensions of power are

  1. \(M{L^2}{T^{ - 2}}\)
  2. \({M}{L^2}{T^{ - 3}}\)
  3. \({M^2}L{T^{ - 3}}\)
  4. \({M^2}L{T^{ - 2}}\)

Answer (Detailed Solution Below)

Option 2 : \({M}{L^2}{T^{ - 3}}\)
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Detailed Solution

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CONCEPT:

  • The rate of work done is called power.
  • It is denoted by P. The SI unit of power is the watt (W).

Power (P) = W / t

W = work done

t = time

EXPLANATION:

Dimensions of force is \(ML{T^{ - 2}}\).

Energy or Work done = Force × Distance 

Dimensions of energy is \(M{L^2}{T^{ - 2}}\).

 The dimensions of power = (Dimension of work) / Time (t) = (\(M{L^2}{T^{ - 2}}\))/T =  \(M{L^2}{T^{ - 3}}\).

Railways Solution Improvement Satya 10 June Madhu(Dia)

Quantities Dimension
Dynamic viscosity M1L-1T-1
Kinematic viscosity L2T−1
Magnetic Flux ML2T-2I-1
Magnetic field M1 T-2 I-1
Power ML2T-3
Torque M1L2T-2
Work ML2T-2
Pressure ML-1T-2
Force M1L1T-2
Surface Tension M1L0T-2
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