A block of mass m and a triangular wedge of mass M move together without slipping due to a pulling force F. The triangular wedge has a slope α. There is no friction between any pair of surfaces. Derive an equation of pulling force.

# A charged solid spherical conductor with a charged solid spherical shell

A solid spherical conductor has charge + Q and radius R. It is surrounded by a solid spherical shell with charge − Q, inner radius 2R, and outer radius 3R. The objects are isolated in space and the electric potential is zero as the distance from the spheres approaches infinity. Point A is at the center of the inner sphere, Point B is located at R, Point C is located at 2R and point D is located at 3R. All distances are from the center of the inner sphere.

Where is the electric potential maximum?

Where is the electric field maximum?

# A system of three objects

A system is composed of three objects with masses m, 5m and 6m. The coefficient of kinetic friction between the objects m, 5m and the surface is 0.5. Find the acceleration of the objects.

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# The light bulbs are connected in series or parallel

Two identical light bulbs are connected to identical batteries in two different ways. First they are connected in series and then in parallel. In which circuit will the bulbs shine brightly? What is the ratio of the power supplied in series to the power supplied in parallel?

# A geostationary satellite

A geostationary satellite is a satellite in geostationary orbit, with an orbital period the same as the Earth’s rotation period. The geostationary orbit is a circular orbit directly above the Earth’s equator.

How high above the Earth’s surface must the geostationary satellite be placed into orbit?

# Magnetic field due to a current in a straight wire

A corner point makes angles θ_{1} and θ_{2} with the ends of a straight wire carrying current I. The distance of the point from the wire is a. What is the

magnetic field at the point?

# The boat is pulled to the shore

A boy stands on a shore and pulls a rope connected to a boat. The velocity of the rope v_{r} is constant. Prove that the closer the boat to the shore, the faster it moves.