A spherical planet has uniform density (π/2)× 104 kg/m3 Find out the minimum period for a satellite in a circular orbit around it in seconds. (Use G = (20/3) × 10-11 (N-m2/kg2))

Question

A spherical planet has uniform density (π/2)× 104 kg/m3 Find out the minimum period for a satellite in a circular orbit around it in seconds. (Use G = (20/3) × 10-11 (N-m2/kg2)) (A) 7500 (B) 3000 (C) 4500 (D) 6000

Tardigrade Admin · Accepted Answer

Time period is minimum for the satellites with minimum radius of the orbit i.e. equal to the radius of the planet. Therefore.

\frac{GM m}{R ^{2}} = \frac{m v ^{2}}{R}

V = \frac{GM}{R}

T_{min} = \frac{2 π R}{\frac{GM}{R}} = \frac{2 π R R}{GM}

using

M = \frac{4}{3} p R^{3} \cdot ρ T_{min} = \frac{3 π}{Gρ}

Using values

T_{min} = 3000 s

Q. A spherical planet has uniform density $\frac{π}{2} \times 1 0^{4} k g / m^{3}$ Find out the minimum period for a satellite in a circular orbit around it in seconds. (Use $G = \frac{20}{3} \times 1 0^{- 11} \frac{N - m ^{2}}{k g ^{2}})$

$7500$

$3000$

$4500$

$6000$

Q. A spherical planet has uniform density 2π​×104kg/m3 Find out the minimum period for a satellite in a circular orbit around it in seconds. (Use G=320​×10−11kg2N−m2​)

7500

3000

4500

6000

Time period is minimum for the satellites with minimum radius of the orbit i.e. equal to the radius of the planet. Therefore. R2GMm​=Rmv2​ V=RGM​​ Tmin​=RGM​​2πR​=GM​2πRR​​ using M=34​pR3⋅ρTmin​=Gρ3π​​ Using values Tmin​=3000s

Q. A spherical planet has uniform density $\frac{π}{2} \times 1 0^{4} k g / m^{3}$ Find out the minimum period for a satellite in a circular orbit around it in seconds. (Use $G = \frac{20}{3} \times 1 0^{- 11} \frac{N - m ^{2}}{k g ^{2}})$

$7500$

$3000$

$4500$

$6000$