AP EAPCET 19-Aug-2021 Shift 2 Paper

Given, speed of ripple of water =v
Surface tension =σ
Density =ρ
Wavelength =λ
As we know that, σ=

Force

Length

and dimensional formula of
σ=

[MLT−2]

[L]

=[ML0T−2]
and dimensional formula of ρ,v and λ are
[ML−3T0],[M0LT−1] and [M0LT0].
Let [σ]=[ρ]a[v]b[λ]c
⇒[ML0T−2]=[ML−3T0]a[M0LT−1]b[M0LT0]c
=[MaL−3a+b+cT−b]
⇒a=1
⇒b=2
⇒−3a+b+c=0
⇒−3+2+c=0
c = 1
∴[σ]=[ρ]1[v]2[λ]1
Hence, σ∝ρv2λ
⇒v2∝

σ

ρλ