The momentum of inertia of a body rotating about a given axis is `12.0 kg m^(2)` in the SI system . What is the value of the moment of inertia in a system of units in which the unit of lengths is `5 cm` and the unit of mass is `10 g`?

Options

A. ` 2.4 xx 10^(3)`
B. `6.0 xx 10^(3)`
C. `5.4 xx 10^(5)`
D. `4.8 xx 10^(5)`

Answer

D

Explanation

` n_(2) = n_(1) ((M_(1))/(M_(2)))^(a) ((L_(1))/(L_(2)))^(b) ((T_(1))/(T_(2)))^( c )`
Dimensional formula of moment of interia ` = [ML^(2) T^(0)]`
:. ` a = 1, b= 2 , c = 0 `
`n_(1) = 12.0 , M_(1) = 1 kg , M_(2) = 10 g `
`L_(1) = 1 m , L_(2) = 5 cm , T_(1) = 1 s, T_(2) = 1 s`
`n_(2) = 12.0 ((1 kg)/( 10 g)) ^(1) ((1 m)/( 5 cm))^(2) ((1 s)/( 1s))^(0)`
` = 12 xx ((1000 g )/( 10 g)) ^(1) (( 100 cm) /(5 cm))^(2) xx 1`
` = 12 xx 100 xx 400 = 4.8 xx 10^(5)`