The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity `(omega)` of a ring are 2%,1% and 1% respectively, then find the maximum percentage error in the measurement of its-
(a) Moment of inertia `(1=(1)/(2)MR^(2))` about its geometric axis.
(b) Rotational kinetic energy `(K=(1)/(2)Iomega^(2))` and
(c) Angular momentum `(J=I omega)` about geometrical axis.

Explanation

(a) Moment of inertia `(I)=(1)/(2)MR^(2)`
`therefore (DeltaI)/(I)xx100=(DeltaM)/(M)xx100+2(DeltaR)/(R)xx100`
`=2%+(2xx1%)=4%`
(b) Rotational kinetic energy `(K)=(1)/(2) I omega^(2)=(1)/(2)MR^(2)omega^(2)`
`therefore (DeltaK)/(K)xx100=(DeltaM)/(M)xx100+2(DeltaR)/(R)xx100+2(Deltaomega)/(omega)xx100`
`=2%+(2xx1%)=6%`
(c) Angular momentum `(J)=I omega=(1)/(2)MR^(2)omega`
`therefore (DeltaJ)/(J)xx100=(DeltaM)/(M)xx100+(Deltaomega)/(omega)xx100`
`=2%+(2xx1%)+1%=5%`