When a particle of mass m is at (x,0), it is attracted toward the origin with a force whose magnitude is k/x^2 where k is some constant. if a particle starts from rest at x = b and no other forces act on it, calculate the work done on it by the time it reaches x = a, 0 < a < b.

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

A10nc charge sits at a point in space where the magnitude of the electric field is 1500 n/c. what will the magnitude of the field be if the 10 nc charge is replaced by a 20 nc charge? assume the system is big enough to consider the charges as small test charges.

How much energy is supplied to each coulomb of charge that flows through a 12-v battery?