Density of a material in GGS system is `4g//cm^(3)`. If length 10 cm and mass 10g are accepted as new system of unit, then density, in new unit system will be……

Options

A. `0.4`
B. 40
C. 400
D. 0.04

Answer

D

Explanation

`n_(1)=3g//cm^(3),n_(2)=?`
`M_(1)=1g,M_(2)=100g`
`L_(1)=1cm,L_(2)=10cm`
`T_(1)=1s" "T_(2)=1s`
Dimensional formula of density `=M^(1)L^(-3)T^(0)`
`:.n_(1)M_(1)^(1)L_(1)^(-3)T_(1)^(0)=n_(2)M_(2)^(1)L_(2)^(-3)T_(2)^(0)`
`:.n_(2)=n_(1)((M_(1))/(M_(2)))^(1)((L_(1))/(L_(2)))^(-3)`
`=4((1)/(100))^(1)((1)/(10))^(-3)`
`=4xx(1)/(100)xx(10)^(3)`
=40 units