Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2024PhysicsElectrostaticsActual

Two beads, each with charge q and mass m , are on a horizontal, frictionless, non-conducting, circular hoop of radius R . One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ ₀ is the permittivity of free space.]

Options

  1. Aq^2 / (4 ₀ R^3 m )
  2. Bq^2 / (32 ₀ R^3 m )
  3. Cq^2 / (8 ₀ R^3 m )
  4. Dq^2 / (16 ₀ R^3 m )

Correct answer

B. q^2 / (32 ₀ R^3 m )

Step-by-step solution

Restoring force = qE ( 2 ) aligned & = qE ( 2 ) R = I & E = Kq (2 R 2 )^2 = 1 4 ₀ q 4 R ^2 ^2 ( 2 ) & 1 4 ₀ qR 4 R ^2 ^2 ( 2 ) ( 2 ) q = mR ^2 aligned For very small, aligned & - q ^2 32 ₀ R ^3 ~m = & ^2= q ^2 32 ₀ mR ^3 aligned Hence option (2)

Practice Electrostatics on Quantrex Academy →

More from Electrostatics

Two charges Q₁ = q and Q₂ = mq are placed at the points P₁(a, b) and P₂(ma, mb) , respectively, in the XY plane, where a, b 0 and m 0, 1 . If V₁ is the potential at a point in the 2026Consider an electric dipole comprising two charges +q and -q each with mass m , separated by a fixed distance d and initially at rest with its dipole moment pointing along i . A un 2026Two point charges q₁=3 , C and q₂=-4 , C are placed at points (2 i +3 j +3 k ) and ( i + j + k ) respectively. Force on charge q₂ is ________ N. ( Take 1 4 ₀ = 9 10^9 SI Units ) 2026The electric potential as a function of x, y is given by V = 5(x^2 - y^2) V. The electric field at a point (2, 3) m is __________ V/m. 2026A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value 2026A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E = 2x i + 3y^2 j + 4 k N/C. The work done in moving the charge is 2026A particle of charge q and mass m is projected from origin with an initial velocity v = ( v₀ 2 x + v₀ 2 y ) . There exists a uniform magnetic field B = B₀ z and a space varying ele 2026A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E ₁=E₀ x . If another electric field E ₂=2E₀( y + z ) is introduced to the s 2026 Full Electrostatics list All JEE Advanced PYQs