Exams › JEE Advanced › Physics
A small sphere of mass 80 g carrying charge q is held 9 m vertically above the centre of a fixed non-conducting sphere of radius 1 m that also carries charge q. When released, the small sphere falls freely until it is repelled and just barely stops before touching the fixed sphere. Given g = 9.8 m/s², the charge q equals 7K micro-coulombs. Find K.
- 1
- 2
- 3
- 4
Correct answer: 2
Solution
The sphere falls from height 9 m above centre to 1 m (surface contact). Height fallen h = 9 - 1 = 8 m. Energy conservation: m*g*h = kₑ*q²*(1/1 - 1/9) = kₑ*q²*(8/9). So m*g = kₑ*q²/9. Then q² = 9*m*g/kₑ = 9*0.08*9.8/(9*10⁹) = 7.056/9*10⁹ ≈ 7.84*10⁻¹⁰ => q ≈ 2.8*10⁻⁵ C but let me redo: q² = m*g*h*9/(kₑ*8) = 0.08*9.8*8*9/(9*10⁹*8) = 0.08*9.8*9/(9*10⁹) = 0.08*9.8/(10⁹) = 0.784*10⁻⁹ => q = sqrt(7.84*10⁻¹⁰) = 2.8*10⁻⁵ C... Hmm that's 28 micro-C. Let me try: q = 7K uC, so K = q/(7 uC). With q = 14 uC, K=2. Let's verify: m*g*h = U_final - U_initial => 0.08*9.8*8 = 9*10⁹*(14*10⁻⁶)²*(1 - 1/9) = 9*10⁹*196*10⁻¹²*(8/9) = 9*10⁹*196*10⁻¹²*8/9 = 8*196*10⁻³ = 1.568. LHS = 0.08*9.8*8 = 6.272. Not matching. Let me reconsider: initial height above SURFACE of sphere = 9 m, so initial height above CENTRE = 10 m. Final = 1 m (surface). h = 9 m fallen. Energy: m*g*9 = kₑ*q²*(1/1 - 1/10) = kₑ*q²*(9/10). So m*g = kₑ*q²/10 => q² = 10*m*g/kₑ = 10*0.08*9.8/(9*10⁹) = 7.84/(9*10⁹) => q = sqrt(8.71*10⁻¹⁰) = 2.95*10⁻⁵ C ≈ 29.5 uC ≈ 7*4.2 uC. K≈4? Let me try: height above centre = 9m, so falls to 1m, falling 8m. m*g*deltaₕ = kₑ*q²*(1/r_f - 1/r_i): 0.08*9.8*8 = 9*10⁹*q²*(1/1-1/9) => 6.272 = 9*10⁹*q²*(8/9) => 6.272 = 8*10⁹*q² => q² = 6.272/(8*10⁹) = 7.84*10⁻¹⁰ => q = 2.8*10⁻⁵ C = 28 uC = 7*4 uC => K = 4.
Related JEE Advanced Physics questions
- Two identical conducting spheres A and B, each of radius R, carry equal charges and are separated by a large distance d (d >> R), exerting a force f0 on each other. A neutral conducting sphere of radius 2R is first touched to sphere A, then touched to sphere B, and finally removed far away. What is the new electrostatic force between A and B?
- Two concentric thin conducting shells of radii a and 2a carry charges Q and -Q respectively. A point charge Q is placed at distance a/2 from the common centre. Which of the following statement(s) is/are correct?
- A uniformly charged non-conducting solid sphere of radius R carries total charge Q. A narrow tunnel is drilled through the sphere along a diameter. A point charge q of mass m is placed at one end of the tunnel (on the surface of the sphere, point A) and released. What is the minimum initial speed v0 that must be given to the charge so that it reaches the other end B (diametrically opposite point on the surface)?
- A long straight wire with linear charge density lambda runs along the axis of a thin hollow metallic cylindrical shell of radius R. The shell has a net linear charge density 2*lambda. Assume lambda > 0. Which of the following are correct?
- Two smooth non-conducting spherical shells, A (charge +Q, mass m) and B (charge -Q, mass 2m), each of radius R, are released from rest on a frictionless surface with their centres 5R apart. Find the speed of shell A just before they collide. (K = 1/(4*pi*epsilon0))
- A charge Q is placed at the centre of a cube. Let phi denote the electric flux due to Q. Which of the following is correct regarding flux through various faces/portions of the cube?
⚔️ Practice JEE Advanced Physics free + battle 1v1 →