Physics - Electrostatics Question with Solution | TestHub
Match the entries of List - I with the systems of List - II:
List - I | List - II |
|---|---|
(A) Magnitude of angular momentum of system about O increases after the instant shown. | (P) A dipole is hinged on a long smooth fixed horizontal wire. A charge Q (A) is threaded on wire and is free to move on the wire. The system comprises of the dipole and point charge. Gravity is absent.  |
(B) The net torque on body A is zero about O at the instant shown. | (Q) A system of two charges and (A) of mass m each are connected by a light rod and kept on smooth level ground. An external uniform electric field is applied as shown. Gravity is present.  |
(C) The net force on negative charge increases in magnitude after the instant shown. | (R) An electron (A) is revolving about a fixed proton in anticlockwise direction. The system comprises of the electron and proton. Gravity is absent.  |
(D) Mechanical energy of the system increases after the instant shown. | (S) System consists of a particle (A) of mass m and charge . It is projected from level ground in presence of constant electric field in vertically upward direction. Gravity is present. (Ignore potential energy of external electrical field.)  |
| (T) System consists of a uniform ring and particle (A) of mass m and charge on its circumference as shown. The ring is in pure rolling on a sufficiently rough horizontal surface. Gravity is present.  |
Options:
Answer:
Solution:
(P) The charge Q is on the dipole's equatorial line, so the electric force on it is vertical and balanced by the wire's normal: net force zero ⇒ torque about O zero - (B). The dipole starts rotating; its angular speed grows from zero, so angular momentum about O grows (A) and the centripetal force on grows from zero (C). Only internal forces: energy constant (D wrong).
(Q) Body A is the charge at O: all forces on it act at O, torque about O is zero - (B). The charge lifts off (), the rod tilts and later drags : the net force on the negative charge grows from zero (C); the angular momentum about O grows as speeds up (A); the external field does positive work: mechanical energy increases (D).
(R) Isolated electron-proton: central force. Torque on the electron about O is zero (B); L, force magnitude and energy are all constant (A, C, D wrong).
(S) Constant net force downward on : torque about O grows as x grows, so increases (A); net force constant (C wrong); the electric force does negative work as the particle rises, so mechanical energy decreases (D wrong); torque nonzero (B wrong).
(T) Pure rolling, no external field: energy conserved (D wrong); gravity on the particle gives nonzero torque about O (B wrong); nothing drives L or the force to grow at the instant shown (A, C wrong).
Hence A - PQS, B - PRS, C - PQ, D - Q.
