An object is moving through liquid. viscous damping force acting on it is proportional to velocity.

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1.Units, Dimensions and Measurement

medium

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

$M{L^{ - 1}}{T^{ - 1}}$

$ML{T^{ - 1}}$

${M^0}L{T^{ - 1}}$

$M{L^0}{T^{ - 1}}$

Solution

(d) $F \propto v \Rightarrow F = kv \Rightarrow [k] = \left[ {\frac{F}{v}} \right] = \left[ {\frac{{ML{T^{ – 2}}}}{{L{T^{ – 1}}}}} \right] = [M{T^{ – 1}}]$

Standard 11

Physics

Which of the following quantities has a unit but dimensionless?

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A quantity $f$ is given by $f=\sqrt{\frac{{hc}^{5}}{{G}}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of

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(JEE MAIN-2020)

The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is

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If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

medium

(JEE MAIN-2022)

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is

Solution

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