Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II:
Column I | Column II | ||
---|---|---|---|
(A) | The force exerted by X on Y has a magnitude $$Mg$$. | (P) | Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity. |
(B) | The gravitational potential energy of X is continuously increasing. | (Q) | Two rings magnets Y and Z, each of mass M, are kept in frictionless vertical plastic stand so that they repel each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity. |
(C) | Mechanical energy of the system X + Y is continuously decreasing. | (R) | A pulley Y of mass $$m_0$$ is fixed to a table through a clamp X. A block of mass M hangs from a string that goes over the pulley and is fixed at point P of the table. The whole system is kept in a lift that is going down with a constant velocity. |
(D) | The torque of the weight of Y about point is zero. | (S) | A sphere Y of mass M is put in a non-viscous liquid X kept in a container at rest. The sphere is released and it moves down in the liquid. |
(T) | A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container. |
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and $$\mu$$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.
Column I | Column II | ||
---|---|---|---|
(A) | $$E=0$$ | (P) | Charge are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon. |
(B) | $$V\ne 0$$ | (Q) | Charges are on a line perpendicular to PQ at equal intervals. M is the midpoint between the two innermost charges. |
(C) | $$B=0$$ | (R) | Charges are placed on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings. |
(D) | $$\mu \ne 0$$ | (S) | Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides. |
(T) | Charges are placed on two coplanar, identical insulating rings are equal intervals. M is the midpoint between the centres of the rings. PQ is perpendicular to the line joining the centres and coplanar to the rings. |