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प्रश्न
The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speedω. Assuming the relation to be \[k = KI^0w^B\] where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is \[\frac{2}{5}M r^2\]
उत्तर
Kinetic energy of a rotating body is K = kI aωb.
Dimensions of the quantities are [K] = [ML2T−2], [I] = [ML2] and [ω] = [T−1].
Now, dimension of the right side are [I]a = [ML2]a and [ω]b = [T−1]b.
According to the principal of homogeneity of dimension, we have:
[ML2T−2] = [ML2]a [T−1]b
Equating the dimensions of both sides, we get:
2 = 2a
⇒ a = 1
And,
−2 = −b
⇒ b = 2
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