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The momentum of inertia of a body rotati...

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`?

A

`2.4xx10^(3)`

B

`6.0xx10^(3)`

C

`5.4xx10^(5)`

D

`4.8xx10^(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
`n_(2)=n_(1)((m_(1))/(m_(2)))^(a)((L_(1))/(L_(2)))^(b)((T_(1))/(T_(2)))^(c)`for moment of mertia `=ML^(2)T^(0)`
`a=1,b=2,c=0," "L_(1)=1m,L_(2)=5cm,T_(1)=T_(2)1s`
`n_(1)=12.0" "M_(1)=1kg" "M_(2)=10g`
`n_(2)=12.0xx((1kg)/(10g))((1m)/(5cm))^(2)((1s)/(1s))=12.0(1000/10)(100/5)^(2)(1)=12.0xx100xx400=4.8xx10^(5)`
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