Question

prove, v^2=u^2+2as using dimension formula?​

Answer 1

Answer and Explanation:

In the given question,

Initial velocity = u

Final velocity = v

Acceleration = a

Displacement = S

Dimensional formula of :

1. Initial velocity = [u] = L T⁻¹
2. Final velocity = [v] = L T⁻¹
3. Acceleration = [a] = L T⁻²
4. Displacement = [S] = L

Hence,

Dimensional formula of

[v²] = (L T⁻¹) ² = L² T⁻²

[u²] = (L T⁻¹) ² = L² T⁻²

[2aS] = L T⁻² * L = L¹⁺¹ T⁻² = L² T⁻²

Therefore,

[v²] = [u²] = [2aS] = L² T⁻²

Hence,

v² = u² + 2aS is dimensionally correct