The density of a material in SI units 128 kg . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is

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Solution

Q.
The density of a material in SI units 128 kg $m^{- 3}$ . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [2019]

1 410

2 640

3 16

4 40

Ans.
(4)

Density $ρ = \frac{M}{L^{3}}$

$n_{1} u_{1} = n_{2} u_{2}$

$∴ 128 [M_{1} L_{1}^{- 3}] = n_{2} [M_{2} L_{2}^{- 3}]$

$∴ n_{2} = 128 [\frac{M_{1}}{M_{2}}] {[\frac{L_{2}}{L_{1}}]}^{3} = 128 \times [\frac{1000}{50}] \times {[\frac{25}{100}]}^{3}$

$= 128 \times 20 \times \frac{1}{64} = 40$

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