Practice question

Given: A satellite orbits a planet at 1.5 × 10⁷ m from its nter with a period of 4 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 = 4 × 3600 = 14400 s, T² = 2.0736 × 10⁸ s² . r³ = (1.5 × 10⁷)³ = 3.375 × 10²¹ m³ . M = frac4 × (3.14)² × 3.375 × 10²¹⁶.67 × 10⁻¹¹ × 2.0736 × 10⁸. M = frac1.331 × 10²³¹.383 × 10⁻² approx 9.63 × 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.