The correct option is C v2∝gλ
Dimensional formula of velocity, v
[v]=[M0L1T−1]
Wavelength, λ
[λ]=[M0L1T0]
Density, ρ
[ρ]=[M1L−3T0]
Acceleration due to gravity, g
[g]=[M0L1T−2]
Let us suppose the relation is
v2∝λagbρc
⇒[v2]=[λagbρc]
⇒[(M0L1T−1)2]=[M0L1T0]a×[M0L1T−2]b×[M1L−3T0]c
⇒[M0L2T−2]=[M(c)L(a+b−3c)T(−2b)]
On comparing, we get,
c=0(1)
a+b−3c=2(2)
−2b=−2(3)
On solving these equations, we get,
a=1,b=1 and c=0
Thus,
v2∝λagbρc⇒v2∝gλ