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JEE Main 201910 JanuaryMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 January
Shift: Morning Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2019 · 10 January · Morning Shift · Physics · Units and Dimensions

The density of a material in SI units is 128kg m ^ - 3 . In certain...

The density of a material in

SI

units is

128kg{m}^{- 3} .

In certain units in which the unit of length is

25cm

and the unit of mass is

50g,

the numerical value of density of the material is:

Options

A $410$
B $16$
C $40$
D $640$

Correct answer

C. $40$

Step-by-step solution

ρ = \dfrac{M}{{L}^{3}}

{n}_{1}{u}_{1} = {n}_{2}{u}_{2}

∴ 128

\left[{M}_{1}{L}_{1}^{- 3}\right] = {n}_{2}\left[{M}_{2}{L}_{2}^{- 3}\right]

<br/><br/>

∴ {n}_{2} = 128 \times

\left[\dfrac{{M}_{1}}{{M}_{2}}\right]{\left[\dfrac{{L}_{2}}{{L}_{1}}\right]}^{3}

= 128 \times

\left[\dfrac{1000}{50}\right] \times {\left[\dfrac{25}{100}\right]}^{3}

<br/><br/>

= 128 \times 20 \times \dfrac{1}{64}

<br/><br/>

= 40

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