Q14 of 35 Page 9

The kinetic energy K of a rotating body depends on its moment

of inertia I and its angular speed ω. Assuming the relation to be K =


kIa ωb where k is a dimensionless constant, find a and b. Moment of


inertia of a sphere about its diameter is Mr2.


K = k Ia ωb


Dimensions of K = [ML2T-2]


Dimensions of I = [ML2]


Dimensions of ω = [T-1]


Dimensionally


[ML2T-2] = [ML2] a [T-1] b


= [ ML2aT-b]


From here 2a = 2 and -2 = -b


So a = 1 and b = 2.


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