wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

If the velocity of water wave v depends upon the wavelength λ, the density of water ρ and the acceleration due to gravity g, then which of the following options depicts correct relation dimensionally?

A
v2λg1ρ1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
v2gλρ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
v2gλ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
v2g1λ3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C v2gλ
Dimensional formula of velocity, v
[v]=[M0L1T1]
Wavelength, λ
[λ]=[M0L1T0]
Density, ρ
[ρ]=[M1L3T0]
Acceleration due to gravity, g
[g]=[M0L1T2]
Let us suppose the relation is
v2λagbρc
[v2]=[λagbρc]
[(M0L1T1)2]=[M0L1T0]a×[M0L1T2]b×[M1L3T0]c
[M0L2T2]=[M(c)L(a+b3c)T(2b)]
On comparing, we get,
c=0(1)
a+b3c=2(2)
2b=2(3)
On solving these equations, we get,
a=1,b=1 and c=0
Thus,
v2λagbρcv2gλ

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon