The moment 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 length 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 inertia = `[ML^(2)T^(0)]`
`:. A= 1, b=2, c=0`
Here, `n_(1)= 12.0, M_(1)= 1kg, M_(2)= 10g`
`L_(1)= 1m, L_(2)= 5cm , T_(1)= 1s, T_(2)= 1s`
`:. n_(2)= 12.0 ((1kg)/(10g))^(1)((1m)/(15cm))^(2)((1s)/(1s))^(0)`
`= 12 xx ((1000g)/(10g))^(1)((100cm)/(5cm))^(2) xx 1 = 12 xx 100 xx 400 = 4.8 xx 10^(5)`