Question

Find the dimensional formula for linear momentum

Answer 1

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linear momentum p is defined to be p = mv, where m is the mass of the system and v is its velocity. The SI unit for momentum is kg.

angular momentum = mass*velocity*radius = [ML∧2T∧-1]

momentum = mass* velocity= [MLT∧-1]

so the ratio will be [M∧0LT∧0]

Answer 2

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It can be solved with help of using dimension concepts .

Dimension of linear momentum, P = [ MLT⁻¹]

Dimension of velocity, v = [LT⁻¹]

Dimension of density, d = [ML⁻³]

Dimension of frequency , f = [T⁻¹]

Let relation between linear momentum , velocity , density and frequency is

P = v^a d^b f^c

MLT⁻¹= [LT⁻¹]^a [ML⁻³]^b [T⁻¹]^c

MLT − 1] = [M b ] [L a−3b ] [T −a−c]

Compare both sides,

b = 1 ,

a - 3b = 1 ⇒ a - 3×1 = 1 ⇒ a = 4

- a - c = -1 ⇒ -4 - c = -1 ⇒ c = -3

Hence , relation is linear momentum, P = velocity^4 . Density/ frequency ^3

Similarly you can got the relation between , surface tension , velocity , density and frequency .

Dimension of surface tension = [MT⁻²]

∴ [MT⁻²] = [LT⁻¹]ᵃ [ML⁻³]ᵇ [T⁻¹]ˣ

= [Mᵇ ][Lᵃ⁻³ᵇ] [T⁻ᵃ⁻ˣ]

Compare both sides,

b = 1

a - 3b = 0 ⇒ a = 3

-a - x = -2 ⇒x = -1

Hence, relation is surface tension = Velocity^3 . Density/ frequency

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