First slide

Types of collision

Question

A satellite of mass ‘m’ is moving in a circular path of radius r around earth has areal velocity ‘A’. If the radius changes by 1%, what will be the change in its areal velocity?

Moderate

A

$0 .75 %$
B

$2 %$
C

$1 .5 %$
D

$0 .5 %$

Solution

$A = \frac{L}{2 m} = \frac{{mωr}^{2}}{2 m} = \frac{2 {πr}^{2}}{2 T} = \frac{{πr}^{2}}{2 {kr}^{3 / 2}} (As T α r^{3 / 2}) ∴ A α {(r)}^{1 / 2} ∴ \frac{ΔA}{A} = \frac{1}{2} . \frac{Δr}{r} = \frac{1}{2} \times 1 % = 0 .5 % .$

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