Question

The velocity of a particle is given by
v = wAcos(wt-kx), where x is position and t is time.
The dimensions of k/w is


(1) [LT-1]
(3) [L2T-2]
(2) [L-1T1]
(4) [L-2T2]​

Answer 1

Answer:

[L⁻¹T¹] option is correct

Explanation:

Given equation of wave = ωΑcos(ωt -kx)

Dimension formula

position (x) = L¹

Time (T) = T¹

As we know that , only like quantities having the same dimensions can be added to or substracted from each other .

∴ [ωt] = [κ] [x]

⟹ κ/ω= [T] /[x]

⟹ κ/ω= [T]/[x]

⟹ k/ω =L⁻¹ T¹

• ∴ option L⁻¹T¹ is correct