Practice question

Given: How much energy is required to move a 100 kg satellite from 4 R_E to 8 R_E from Earth’s nter? ( M_E = 6 × 10²⁴ kg, R_E = 6.4 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg² ) These values define the system as per NCERT data. Formula: Δ E = -G M_E m (1/r_2 - 1/r_1). This is the standard NCERT relation for this phenomenon. Substitution & Calculation: r_1 = 2.56 × 10⁷ m, r_2 = 5.12 × 10⁷ m . Δ E = -6.67 × 10⁻¹¹ × 6 × 10²⁴ × 100 (1/5.12 × 10⁷- 1/2.56 × 10⁷) . Δ E = -4.002 × 10¹⁶(-1.953 × 10⁻⁸) approx 7.82 × 10⁸ J . 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.