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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. |
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Answer» (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%` |
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