SATHEE: Physics And Measurement Question 68

Physics And Measurement Question 68

Question: The velocity of water waves $v$ may depend upon their wavelength $λ$ , the density of water $ρ$ and the acceleration due to gravity $g$ . The method of dimensions gives the relation between these quantities as

[NCERT 1979; CET 1992; UPSEAT 2000]

Options:

A) $v^{2} r g$

B) $v^{2} \propto g λ ρ$

C) $v^{2} \propto g λ$

D) $v^{2} \propto g^{- 1} λ^{- 3}$

Show Answer

Answer:

Correct Answer: C

Solution:

Let $v^{x} = k g^{y} λ^{z} ρ^{δ} .$ Now by substituting the dimensions of each quantities and equating the powers of M, L and T we get $δ = 0$ and $x = 2, y = 1, z = 1$ .

Physics And Measurement Question 68

Question: The velocity of water waves $v$ may depend upon their wavelength $λ$ , the density of water $ρ$ and the acceleration due to gravity $g$ . The method of dimensions gives the relation between these quantities as

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Physics And Measurement Question 68

Question: The velocity of water waves v may depend upon their wavelength λ , the density of water ρ and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The velocity of water waves $v$ may depend upon their wavelength $λ$ , the density of water $ρ$ and the acceleration due to gravity $g$ . The method of dimensions gives the relation between these quantities as