A. An insulating sphere with radius a has a uniform charge density rho. The sphere isnot centered at the origin but at . Show that the electric field inside the sphere is given by E= rho(r-b)3/εo. b. An insulating sphere of radius R has a spherical holeof radius a located within its volume and centered adistance b from the center of the sphere. The solid partof the sphere has a uniform volume charge density rho. Find the magnitude and direction of the electric field E inside the hole, and show that is uniform over the entire hole.

Aparticle travels in a circular orbit of radius 21 m. its speed is changing at a rate of 23.1 m/s2 at an instant when its speed is 37.2 m/s. what is the magnitude of the acceleration (in m/s? ) of the particle?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Within a pendulum, as potential energy decreases, energy increases. a. heat b. kinetic c. frictional d. gravitational