The density of material in CGS system of units is `4gcm^(-3)`. In a system of units in which unit of length is 10 cm and unit of mass is 100 gm, then the value of density of material will be

Options

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

Answer

b

Explanation

Mass `M = rho V rArr rho = (M)/(V) = (M)/(L^(3))`
We are given `rho = 4 g// cm^(3)`
If unit of mass is `100g` and the unit distance is `10 cm`
`=(4((100g)/(100)))/(((10)/(10) cm)^(2) ) = (((4)/(100)))/(((1)/(10))^(3)) ((100g))/((10g))`
`= 40g cm^(-1)`
`((M_(1))/(M_(2)))((L_(1))/(L_(2)))^(-3) = 4 ((1)/(100)) ((1)/(10))^(-3)`
`= 40`