In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x form the pole P. The student looks at the pin and its inverted image form a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right, oh the object pin. Then,

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' form the centre P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, with the separation between them becomes 2x, is

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinder are initially electrically neutral.

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,