NEET UG 2015 — Physics Mechanics

2015mcqhard

If dimensions of critical velocity, ${v}_{c}$ of a liquid flowing through a tube are expressed as $[{\eta }^{x}{\rho }^{y}{r}^{z}]$ , where, $\eta , \rho$ and $r$ are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of $x$ , $y$ and $\text{z}$ are given by

Official previous-year question

Held on 30 Apr 2015 · Verified 9 Jul 2026.

Options

A
$-1, -1, 1$
B
$-1, -1, -1$
C
$1, 1, 1$
D
$1, -1, -1$

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Solution

Dimensions of velocity, coefficient of viscosity and density are,

$[v]=[{\mathrm{LT}}^{-1}]$

$[\eta ]=\frac{[F]}{[A\frac{dv}{dx}]}=\frac{[{\mathrm{MLT}}^{-2}]}{[{L}^{2}][{T}^{-1}]}=[{\mathrm{ML}}^{-1}{T}^{-1}]$

$[\rho ]=[{\mathrm{ML}}^{-3}]$

Now, $[v]={[\eta ]}^{x}{[\rho ]}^{y}{[r]}^{z}$

$\Rightarrow [{\mathrm{LT}}^{-1}]={[{\mathrm{ML}}^{-1}{T}^{-1}]}^{x}{[{\mathrm{ML}}^{-3}]}^{y}{[L]}^{z}$

Now, by using dimensional homogeneity, we will get,

${M}^{0}={M}^{(x+y)}$

$\Rightarrow y=-x$

For $T$ ,

$x=1$

$\Rightarrow y=-x=-1$

For $L$ ,

$1=-x-3y+z$

$\Rightarrow z=-1$

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Solution

Dimensions of velocity, coefficient of viscosity and density are,

$[v]=[{\mathrm{LT}}^{-1}]$

$[\eta ]=\frac{[F]}{[A\frac{dv}{dx}]}=\frac{[{\mathrm{MLT}}^{-2}]}{[{L}^{2}][{T}^{-1}]}=[{\mathrm{ML}}^{-1}{T}^{-1}]$

$[\rho ]=[{\mathrm{ML}}^{-3}]$

Now, $[v]={[\eta ]}^{x}{[\rho ]}^{y}{[r]}^{z}$

$\Rightarrow [{\mathrm{LT}}^{-1}]={[{\mathrm{ML}}^{-1}{T}^{-1}]}^{x}{[{\mathrm{ML}}^{-3}]}^{y}{[L]}^{z}$

Now, by using dimensional homogeneity, we will get,

${M}^{0}={M}^{(x+y)}$

$\Rightarrow y=-x$

For $T$ ,

$x=1$

$\Rightarrow y=-x=-1$

For $L$ ,

$1=-x-3y+z$

$\Rightarrow z=-1$

NEET UG 2015 — Physics Mechanics

Options

Did you get this right?

Solution

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NEET UG Mechanics in other years

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NEET UG 2015 — Physics Mechanics

Options

Did you get this right?

Solution

Your note

NEET UG Mechanics in other years

More NEET UG Mechanics questions

Other Physics topics for NEET UG

Electromagnetism

Modern Physics

Thermodynamics

Optics

Waves & Oscillations

Keep practicing Mechanics