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

Question

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 (A) increase by 1 % (B) increase by 0.5 % (C) decrease by 1 % (D) decrease by 0.5 %

Tardigrade Admin · Accepted Answer

v propto (1/√r) % increase in speed =(1/2) ( % decrease in radius) =(1/2)(1 %)=0.5 % i.e., speed will increase by 0.5 %.

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

increase by $1%$

increase by $0.5%$

decrease by $1%$

decrease by $0.5%$

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

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

increase by 1%

increase by 0.5%

decrease by 1%

decrease by 0.5%