The dinesity of meterial in CGS system of mass is `4g cm^(3)` in a system of unit in which unit of length is `10 cm` and unit of mass is `100g` the value of density of meterial will be

Options

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

Answer

D

Explanation

(4) Dimensions of density : `ML^(-3)`
`n_(1) u_(1) = n_(2) u_(2)`
`n_(2) = n_(1) (u_(1))/(u_(2)) = n_(1) [(M_(1))/(M_(2))] [(L_(1))/(L_(2))]^(-3)`
Here, `n_(1) = 4, M_(1) = 1 g, L_(1) = 1 cm`
`M_(2) = 100 g, L_(2) = 10 cm`
`n_(2) = 4 [(1)/(100 g)] [(1cm)/(10 cm)]^(-3)`
`= 4 ((1)/(100)) (10)^(3) = 40`