Units & Dimensions

JEE Main level, single correct, medium

16 of 149

Question 16 of 149

The density of a material in SISI units is 128kgm−3.128kg{m}^{-3}. In certain units in which the unit of length is 25cm25cm and the unit of mass is 50g,50g, the numerical value of density of the material is:

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Answer: (C) 4040

ρ=ML3\rho =\dfrac{M}{{L}^{3}}

n1u1=n2u2{n}_{1}{u}_{1}={n}_{2}{u}_{2}

∴128[M1L1−3]=n2[M2L2−3]∴128\left[{M}_{1}{L}_{1}^{-3}\right]={n}_{2}\left[{M}_{2}{L}_{2}^{-3}\right]

∴n2=128×[M1M2][L2L1]3∴{n}_{2}=128\times \left[\dfrac{{M}_{1}}{{M}_{2}}\right]{\left[\dfrac{{L}_{2}}{{L}_{1}}\right]}^{3}

=128×[100050]×[25100]3=128\times \left[\dfrac{1000}{50}\right]\times {\left[\dfrac{25}{100}\right]}^{3}

=128×20×164=128\times 20\times \dfrac{1}{64}

=40=40

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