QJEEM19Ph2681: JEE Main 2019 Physics - Class 11 JEEM19Ph2681 Solution: The density of a material in SI units is 128 kg m –3 . In…

Here given that

density of a material in SI units is 128 kg m^–3

And a new unit system is introduced where 1 unit of length = 25 cm and 1 unit of mass = 50 g

You should know that, physical quantity is same in any unit system. And to calculate a physical quantity yo should know two things

(1) numerical value of the physical quantity (n)

(2) unit of the physical quantity (u)

And n $$\times$$ u = constant in any unit system.

Here in SI unit system,

n₁ = 128

u₁ = kg/m³

And in new unit system,

n₂ = ?

u₂ = 50gm/(25cm)³

As n₁u₁ = n₂u₂

$$\therefore$$ 128 $$\times$$ (kg/m³) = n₂ $$\times$$ 50gm/(25cm)³

$$\Rightarrow$$ 128 $$\times$$ $$\frac{1000gm}{{\left(100cm\right)}^3}$$ = n₂ $$\times$$ $$\frac{50gm}{{\left(25cm\right)}^3}$$

$$\Rightarrow$$ n₂ = 128 $$\times$$ $$\frac{20}{4^3}$$ = 40