Question

A satellite is orbiting round the earth at a height $h$ above the surface of the earth$.$ If this distance h is increased$,$ the period of satellite will :

• A. decrease
• B. increase
• C. remain unaffected
• D. become zero

Answer 1

Answer: (B)

increase

Centripetal force$=$gravitational force

$\Rightarrow \frac{m{v}^2}{h}=\frac{G{m}_{e}m}{h^2}$

$\Rightarrow v=\sqrt{\frac{G{m}_e}{h}}$

Time period 'T'$=\frac{distance}{velocity}$

$=\frac{2\pi h}{v}$

$=\frac{2\pi h}{{\left(\frac{G{m}_e}{h}\right)}^{1/2}}$

$\Rightarrow T=\frac{2\pi }{(4m_e{)}^{1/2}}\times h^{3/2}$

$\Rightarrow T\propto h^{3/2}$

$\Rightarrow$ If height 'h' is increased, time period 'T' will increase.