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2015-09-25T15:04:25+05:30

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  v = orbital velocity        we know  g = G M / R²
  d  = 3400 + 6400 km = 10000 km

 gravitational force = centripetal force
   G M m / d²  =  m v² / d
        v² = G M / d  = g R² / d
        v = R √(g/d)

   ω = angular velocity =  v / R = √(g/d)
   T = time period = 2π/ ω  = 2 π √(g/d)

 substitute the values to get answers.
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2015-09-28T22:37:45+05:30
Distance of artificial satellite (d)= 3400 km
Radius of earth(R) = 6400 km = 6.4×10⁶ m
Radius of orbit(r) = R+d = 10,000 km = 10⁷ m
g = 9.8 m/s²
Orbital velocity, V_o=\ ?
Period of revolution, T = ?

(i) Orbital velocity

V_o= \sqrt{ \frac{GM}{r} }= \sqrt{ \frac{GM}{r} \times \frac{R^2}{R^2} }= \sqrt{ \frac{GM}{R^2} \times \frac{R^2}{r} }= \sqrt{g\times \frac{R^2}{r} }

\Rightarrow V_o= \sqrt{9.8 \times \frac{(6.4 \times 10^6)^2}{10^7} } \\ \\\Rightarrow V_o= \sqrt{40.14 \times 10^6 } \\ \\ V_o=\boxed{6.33 \times 10^3\ m/s}

(ii) Time period
T= \frac{2 \pi r}{V_o} = \frac{2 \times 3.14 \times 10^7}{6.33 \times 10^3} =\boxed{9.93 \times 10^3\ seconds}
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