Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
Gravitational force between two students
m₁ = 60 kg, m₂ = 50 kg, r = 1 m, G = 6.67 × 10⁻¹¹ N m² kg⁻².
F = Gm₁m₂/r² = 6.67 × 10⁻¹¹ × 60 × 50 / 1²
F = 2.0 × 10⁻⁷ N — about 1% of a mosquito's weight, which is why you never feel it.
Mass of the Earth from g, R and G
g = 9.8 m/s², R = 6.4 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m² kg⁻².
g = GM/R² ⟹ M = gR²/G = 9.8 × (6.4 × 10⁶)² / 6.67 × 10⁻¹¹
M = 9.8 × 4.096 × 10¹³ / 6.67 × 10⁻¹¹ = 6.0 × 10²⁴ kg
Orbital speed and period of a low-orbit satellite
For an orbit skimming the surface, gravity = centripetal force: mg = mv²/R.
v = √(gR) = √(9.8 × 6.4 × 10⁶) = √(6.27 × 10⁷) = 7.9 × 10³ m/s ≈ 7.9 km/s
T = 2πR/v = 2π × 6.4 × 10⁶ / 7.9 × 10³ ≈ 5.1 × 10³ s ≈ 84 minutes
Value of g on Mount Everest (h = 8848 m)
For h ≪ R use g_h ≈ g(1 − 2h/R).
g_h = 9.80 (1 − 2 × 8848 / 6.4 × 10⁶) = 9.80 (1 − 0.00277)
g_h = 9.77 m/s² — even on the world's highest peak g falls by only 0.3%.
⚠ For large heights (h = R) use the exact formula g_h = gR²/(R+h)² — at h = R it gives g/4, NOT zero.