Question 179: Units , Dimensions and Error Analysis

Question

The density of a material in SI units is 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 -

Accepted Answer

Here given that
density of a material in SI units is 128 kg m
Ã¢ÂÂ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 $$ 	imes $$ u = constant in any unit system.
Here in SI unit system,
n
1
= 128
u
1
= kg/m
3
And in new unit system,
n
2
= ?
u
2
= 50gm/(25cm)
3
As n
1
u
1
= n
2
u
2
$$ 	herefore $$ 128 $$ 	imes $$ (kg/m
3
) = n
2
$$ 	imes $$ 50gm/(25cm)
3
$$ \Rightarrow $$ 128 $$ 	imes $$ $${{1000\,gm} \over {{{\left( {100\,cm} ight)}^3}}}$$ = n
2
$$ 	imes $$ $${{50\,gm} \over {{{\left( {25\,cm} ight)}^3}}}$$
$$ \Rightarrow $$ n
2
= 128 $$ 	imes $$ $${{20} \over {{4^3}}}$$ = 40

Answer

40

Answer

640

Answer

16

Answer

410

Units , Dimensions and Error Analysis

The density of a material in SI units is 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 -

Choose the correct answer: