Study Guides/Physics/Dimensional Formula of Acceleration
Study Guide · Physics

Dimensional Formula of Acceleration

Acceleration is one of the most basic physical quantities in kinematics. It measures how fast the velocity of an object is changing. Deriving its dimensional formula is one of the first things you learn in Class 11 Physics.

Question (Click to Flip)

Is the dimensional formula for acceleration due to gravity (g) different?

Answer

No. Acceleration due to gravity is still an acceleration, so its dimensional formula is exactly the same: $[M^0 L^1 T^{-2}]$.

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Key Facts

The SI unit for acceleration is meters per second squared ($m/s^2$).

Since mass is not involved in calculating pure acceleration, its dimension for Mass (M) is zero ($M^0$).

1. The Base Formula

The fundamental formula for Acceleration ($a$) is: Acceleration = $\frac{\text{Change in Velocity}}{\text{Time}}$

2. Breaking it down

To find the dimension, we first need the dimension of Velocity.

  • Velocity = $\frac{\text{Displacement (Length)}}{\text{Time}}$
  • Dimension of Velocity = $\frac{[L]}{[T]} = [L^1 T^{-1}]$

3. The Final Derivation

Now, substitute the dimension of velocity back into the acceleration formula:

  • Acceleration = $\frac{[L^1 T^{-1}]}{[T]}$

Bring the Time ($T$) from the denominator to the numerator:

  • $[L^1 T^{-1}] \times [T^{-1}]$
  • Combine the exponents ($-1 - 1 = -2$)

Final Dimensional Formula = $[M^0 L^1 T^{-2}]$

Questions and Answers

Is the dimensional formula for acceleration due to gravity (g) different?+

No. Acceleration due to gravity is still an acceleration, so its dimensional formula is exactly the same: $[M^0 L^1 T^{-2}]$.

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