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The dimensional formula for the rate of change of momentum of a moving body is

  • A.\(ML^{2}T^{-2}\)
  • B.\(MLT^{-1}\)
  • C.\(ML^{-1}T^{-1}\)
  • D.\(MLT^{-2}\)
  • E.\(M^{0}LT^{-1}\)

Answer: D

The dimensional formula is \(MLT^{-2}\).

By Newton's second law the rate of change of momentum is force. Momentum is mass times velocity, \([MLT^{-1}]\), and dividing by time gives \([MLT^{-2}]\), the dimensions of force.

\(MLT^{-1}\) is momentum itself, not its rate of change. \(ML^{2}T^{-2}\) is energy, \(ML^{-1}T^{-1}\) is the coefficient of viscosity, and \(M^{0}LT^{-1}\) is velocity.

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