A satellite is moving around the with speed v in a circular orbit of radius r. If the orbit radius is decreased by $1 %$ , its speed will

$I n c r e a s e b y 1 %$

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$I n c r e a s e b y 0.5 %$

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$D e c r e a s e b y 1 %$

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$D e c r e a s e b y 0.5 %$

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Solution

The correct option is B
$I n c r e a s e b y 0.5 %$

Orbital velocity $v = \sqrt{\frac{G m}{r}} ∴ v \propto \frac{1}{\sqrt{r}}$ [If r decreases then v increases]

Percentage change in $v = \frac{1}{2}$ (Percentage change in r) $= \frac{1}{2} (1 %) = 0.5 %$

$∴$ orbital velocity increases by $0.5 %$ .

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