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### Ray Optics: Refraction

Q- A jewel thief hides a diamond by placing it at the bottom of a public swimming pool. He places a circular raft on the surface of the water directly above the diamond as shown in the figure. The surface of water is smooth and the pool is 2.0m deep. Find the minimum diameter d of raft if it is to prevent the diamond from being seen by the people not in wager. (Refractive index of water = 1.4) ### Thermodynamics: Heat Pump

Q- A heat pump is used to maintain a house at a constant temperature of 230C. The house is losing heat to the outside air through the walls and the windows at a rate of 60000 kJ/h and the energy generated within the house from lights and appliances amounts to 5000 kJ/h. For COP of 2.5, determine the power input to the heat pump.

Solution:

### Mechanics: Conservation of Energy

Q- A roller coaster car of mass 1000 kg is riding along a track from point A to point C as in figure. (g = 10 m/s2)

(a) Assuming no friction between the track and the car, what is the speed of the car at the top of first hill A?

(b) What is the speed of the car at the top of second hill B?

(c) What is the maximum speed of the car along the track?

(d) Assume there is friction and the car start with the same speed at A. If the work done against friction from A to C is 50000 J, will the car still reach C and if so what is its velocity at C? Solution:

### Electrostatics: Dielectric and Polarization

Q- Two parallel conducting plates are separated by distance d and the potential difference between them is V. A dielectric slab of dielectric constant k and uniform thickness nearly d is inserted between the plates. As the dielectric slab is not smooth enough, it touches the plates in some regions and there are some tiny gaps. Neglecting edge effects

(a) Find the electric filed in the dielectric and in the tiny gaps

(b) Find the charge density on the plate at parts in contact with the slabe and at the parts of gaps.

(c) Find the polarization charge density on the dielectric surface.

Solution:

### Force: Equilibrium

Q- A patient in therapy has a forearm that weighs 20.5 N and lifts a 112.0 N weight. The only other significant forces on his forearm come from the biceps muscle (which acts perpendicularly to the forearm) and the force at the elbow. If the biceps produce a pull of 232 N when the forearm is raised 43° above the horizontal, find the magnitude and direction of the force that the elbow exerts on the forearm.

Solution: