In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q₁ $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q₂ $$\mu$$C.



The magnitude of q₂ is ________________.

Two point charges $$-$$Q and +Q/$$\sqrt 3 $$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.



The value of R is __________ meter.

Two point charges $$-$$Q and +Q/$$\sqrt 3 $$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.



The value of b is __________ meter.

A horizontal force F is applied at the center of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $$\mu$$. The center of mass of the object has an acceleration a. The acceleration due to gravity is g. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?