Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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 = K I 0 W B Where K is a Dimensionless Constant, Find a and B. Moment - Physics

Sum

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  $\frac{2}{5}M r^2$

#### Solution

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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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 1 Introduction to Physics
Exercise | Q 14 | Page 10