Density of a material in SI, units is 128, kg, m^{-3} . In certain units in which unit of length is

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1.Units, Dimensions and Measurement

medium

The density of a material in $SI\, units$ is $128\, kg\, m^{-3}$. In certain units in which the unit of length is $25\, cm$ and the unit of mass $50\, g$, the numerical value of density of the material is

A$40$

B$16$

C$640$

D$410$

(JEE MAIN-2019)

Solution

$\begin{array}{l}
\frac{{128kg}}{{{m^3}}} = \frac{{125\left( {50g} \right)\left( {20} \right)}}{{{{\left( {25cm} \right)}^3}{{\left( 4 \right)}^3}}}\\
= \frac{{128}}{{64}}\left( {20} \right)units\\
= 40units
\end{array}$

Standard 11

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(AIIMS-2017)

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
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medium

(JEE MAIN-2022)

The density of a material in $SI\, units$ is $128\, kg\, m^{-3}$. In certain units in which the unit of length is $25\, cm$ and the unit of mass $50\, g$, the numerical value of density of the material is

Solution

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