Question

The dimensions of area x velocity have the
same dimensions as

(a) Volume
(b) Energy
(c) momentum
(d) Volume of liquid flowing per
second​

Answer 1

Given : dimensions of area * velocity

To Find :   The dimensions of area * velocity have the same dimensions as

Volume

Energy

Momentum

Volume of liquid flowing per second​

Solution :

Dimension of area = L²

Dimension of Velocity = LT⁻¹

dimensions of area * velocity   =L² *  LT⁻¹

= L³T⁻¹

L³  is dimension of volume

L³T⁻¹  is dimension of volume  per sec

Hence Volume of liquid flowing per second​  is correct answer

The dimensions of area * velocity have the same dimensions as Volume of liquid flowing per second​  =  L³T⁻¹

Dimension of volume  =  L³

Dimension of energy :  = M L² T⁻²

Dimension of momentum = MLT⁻¹

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Answer 2

Dimensional Analysis Steps for this question:

$\bigg[area \times velocity\bigg]$

$= \bigg[({M}^{0} {L}^{2}{ T}^{0} ) \times ({M}^{0} L{T}^{ - 1}) \bigg]$

$= \bigg[{L}^{3} {T}^{ - 1}\bigg]$

$= \bigg[ \dfrac{{L}^{3}}{T}\bigg]$

$= \bigg[ \dfrac{volume}{time}\bigg]$

So, [area × velocity] has same dimensions is [volume of fluid flowing per unit time].

OPTION d) IS CORRECT !