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Q.

The moment of inertia of a particle rotating about a given axis is 12.0 kg m2 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?

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a

2.4×103

b

6.0×103

c

5.4×105

d

4.8×105

answer is D.

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Detailed Solution

n2=n1M1M2aL1L2bT1T2c Dimensional formula of moment of inertia =ML2T0∴ a=1,b=2,c=0n1=12.0,M1=1kg,M2=10gL1=1m,L2=5cm,T1=1s,T2=1sn2=12.01kg10g11m5cm21s1s0=12×1000g10g1100cm5cm2×1=12×100×400=4.8×105

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The moment of inertia of a particle rotating about a given axis is 12.0 kg m2 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?