If $A$ is the areal velocity of a planet of mass $M$, its angular momentum is

If $A$ is the areal velocity of a planet of mass $M$, its angular momentum is
  1. $\frac{M}{A}$
  2. $2MA$
  3. $A^2 M$
  4. $A M^2$

Solution

Areal velocity $A=\frac{1}{2} R^2 \omega$ $\therefore \quad$ Multiplying by $M$ on both sides $ \begin{aligned} M A & =\frac{1}{2} M R^2 \omega \\ M A & =\frac{1}{2} I \omega \end{aligned} $ $I=$ moment of inertia. $ M A=\frac{1}{2} L $ where, $L=$ angular momentum $ \begin{array}{rlrl} & =I \omega \\ \therefore & L & =2 M A \end{array} $

Asked in: AP EAMCET 2002

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