Question

Displacement of a body with respect to time s=At-B÷t^2 find the dimension of A÷B

Answer 1

Answer:

Dimension of A/B = T⁻³

Explanation:

Given that,

$S = At + \frac{B}{t^{2} }$

Since $S,At,\frac{B}{t^{2} }$ are all added or subtracted they all have the same unit that is,

Unit of S = Unit of At = Unit of $\frac{B}{t^{2} }$

[S] = [At] = [$\frac{B}{t^{2} }$]

Therefore,

[S] = [At]

L = [A] T

[A] = L T⁻¹

[S] = [$\frac{B}{t^{2} }$]

L = [B] T⁻²

[B] = L T²

Hence,

[A/B] = (L T⁻¹) / (L T²)

[A/B] = L¹⁻¹  T⁻¹⁻²

[A/B] = L⁰ T⁻³ = T⁻³