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 0.5% Decrease by 1%

Increase by 0.5%

Orbital velocity $V = \sqrt {\frac{Gm}{r}}$ $V' =  \sqrt {\frac{Gm}{r - 0.01 r}}=  \sqrt {\frac{Gm}{r}}(1 + \frac{0.01}{2}) = V + 0.005 V $ $\Rightarrow \Delta V = 0.005 V$ $\Rightarrow \text{Speed will increase by 0.5%}$