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

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

Gravitation

Solution:

$v \propto \frac{1}{\sqrt{r}}$
$\%$ increase in speed $=\frac{1}{2}$ (\% decrease in radius)
$=\frac{1}{2}(1 \%)=0.5 \%$
i.e., speed will increase by $0.5 \%$.