Practice question

Given: A satellite orbits at 1.2 × 10⁷ m from a planet’s nter with period 3 hours. What is the planet’s mass? ( G = 6.67 × 10⁻¹¹ N m²/kg² ) These values define the system as per NCERT data. Formula: M = 4π² r³/G T². This is the standard NCERT relation for this phenomenon. Substitution & Calculation: T = 3 × 3600 = 10800 s, T² = 1.166 × 10⁸ s² . r³ = (1.2 × 10⁷)³ = 1.728 × 10²¹ m³ . M = frac4 × (3.14)² × 1.728 × 10²¹⁶.67 × 10⁻¹¹ × 1.166 × 10⁸. M = frac6.82 × 10²²⁷.78 × 10⁻³ approx 8.77 × 10²⁴ kg . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.