Question

The density of a material in CGS system of units is 4g cm-³. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be...?
1) 0.04


2) 40


3) 0.4


4) 400​

Answer 1

$\sf\underline{Solution:}$

Here , the density of the material is 4g cm³ but it is not given in CGS system.

$\sf{As\:we\:know\:that:}$

$\sf\bold{Density=}$ $\sf\dfrac{Mass}{Volume}$

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$\sf{Now,according \: to \:the\:question:}$

$\sf\small{Density\:of\:the\:material=4}$ $\sf\dfrac{g}{cm^2}$

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$\sf{It\:is\:given\:that:}$

In the system of units the mass is 100gram.

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Hence,

$\sf{The\:mass\:unit\:for\:4g=}$ $\sf\dfrac{4}{100}$ $\sf{units}$

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In the system of units,the length is 10cm.

Henceforth,

$\sf\small{The\:length \:for\:1cm\:units=}$ $\sf\dfrac{1}{10}$ $\sf{units}$

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☆ Substitute the required values in the given formula-

$\sf\purple{Density=}$ $\sf\dfrac\purple{Mass}\purple{volume}$

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$\sf\underline\bold{Density\:of\:the\:material:}$

= $\sf\dfrac{4/100}{1/10^3}$ $\sf\bold{units}$

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= $\sf\dfrac{4/100}{1/1000}$ $\sf\bold{units}$

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= $\sf\dfrac{4000}{100}$ $\sf\bold{units}$

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$\sf\underline\bold\blue{=40\:units}$

$\sf\small{Therefore,option\:2nd\:is\:correct!}$

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