Question

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

• A. Increases by $1\%$
• B. Increases by $0.5\%$
• C. Decreases by $1\%$
• D. Decreases by $0.5\%$

Answer 1

Answer: (B)

Increases by $0.5\%$

When satellite moves around the earth its speed is given by $V=\sqrt{\frac{GM}{R}}$

Now,

on applying error estimation.

$\frac{\Delta V}{V}=\frac{1}{2}\frac{\Delta r}{R}$

$\Rightarrow \frac{\Delta V}{V}\times 100=0.5$%

So, Velocity will increase by $0.5$% as velocity is inversely proportional to the radius.