Two equal charges q₀ = +2 μC, each of mass 20 g, are placed on a frictionless 30° incline as shown. For equilibrium, h = x × 10⁻³ m. Find x. Take k = 9 × 10⁹ N m² C⁻² and g = 10 m s⁻². Image
Physics · Circular Motion
JEE Mains 11 April 2023 Shift 1 Morning Shift

Question

Two equal charges q₀ = +2 μC, each of mass 20 g, are placed on a frictionless 30° incline as shown. For equilibrium, h = x × 10⁻³ m. Find x. Take k = 9 × 10⁹ N m² C⁻² and g = 10 m s⁻². Image

Physics · Circular Motion

JEE Mains 11 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

For either charge, electrostatic repulsion balances the component of weight along the incline: kq₀²/r² = mg sin30°. From the geometry, r = h/sin30° = 2h. Thus kq₀²/(4h²) = mg/2. Substituting q₀ = 2×10⁻⁶ C, m = 0.020 kg: h² = 9×10⁻², so h = 0.30 m = 300×10⁻³ m. Final value: 300