By definition of perfectly inelastic, the objects move off together with one common velocity, v ², after the collision. By conservation of linear momentum,

The correct answer is (B). This statement is one of Einstein抯 postulates to the theory of relativity.

The frequency is unchanged, but because the speed of light in diamond is less than in air, the wavelength of the light in diamond is shorter than its wavelength in air.

The speed of a transverse traveling wave on a stretched rope is given by the equation v = . Therefore

The correct answer is (C). When the variable resistor is moved toward the right, more of the resistance value of the variable resistor is bypassed which means there is less resistance in the circuit. A decrease in the resistance of a circuit allows more current to flow (Ohm's Law). Since there is more current flowing in the circuit the fan has more current flowing through it too, and the fan runs faster.

The correct answer is (B). The toy rocket achieves zero velocity at the exact top of its flight when it is not moving upward nor is it moving downward. It is constantly accelerated toward the earth while it is in free fall.

First, let's figure out how much heat is required to bring the water to its boiling point.

The correct answer is (B). The angular acceleration is found by dividing the change in angular velocity by the change in time:

The correct answer is (D). The same car traveling at twice the velocity has four times the energy. Constant frictional force from the tires will therefore require four times the stopping distance. The car moving at the lower rate only requires 1/4 the stopping distance.

The correct answer is (E). For any value of the vector V and V , they are equal in magnitude to one another. Whether they act in the same or opposite directions from one another, all the choices are possible except the value of 4 times V.

5 C Both electric force and electric field obey inverse square laws. The equation for electric force is F = , and the equation for electric field is E = . Thus, both of these would be one-quarter as great at twice the distance. However, electric potential is just an inverse. The equation for electric potential is (notice that the r is not squared). Thus, at twice the distance, it would be half as great. Thus, only Roman numeral III is true.

The correct answer is (C). The tangential velocity is the product of the angular velocity and the radius of the object or the person from the center of the rotating device. Both children have the same angular velocity, but the child on the pony is farther from the center of the merry-go-round.

The correct answer is (C). The diver needs to complete the rotations as quickly as possible. The tuck position reduces the moment of inertia of the diver's body, allowing the diver to spin at a higher rate.

I is false: The magnetic field lines due to a current-carrying wire encircle the wire in closed loops. II is also false: Since the magnetic force is always perpendicular to the charged particle's velocity vector, it can do work on the charged particle; therefore, it cannot change the particle's kinetic energy. III, however, is true: If the charged particle's velocity is parallel (or antiparallel) to the magnetic field lines, then the particle will feel no magnetic force.

The correct answer is (C). The rocket sled is already moving. The two rocket engines apply two (different pairs) of forces of equal magnitude to the same object but in different directions. There is therefore no unbalanced force and the sled continues in its state of motion.

The correct answer is (C). The centripetal acceleration is found with the following equation:

The correct answer is (B). According to Ohm's Law, the current is equal to I = V/r. Solving for the current, we have 12V/20ohm = .6 ampere.

The correct answer is (D). Rutherford found that most of the mass of an atom is concentrated in the nucleus of the atom.

The correct answer is (E). The number of protons added to the number of neutrons is equal to the mass number of an atom. The mass is represented by the letter A.

The correct answer is (C). An adiabatic process is one during which no heat enters or leaves the system. Work is done on the system (the compression of the gas) that keeps the heat content of the system constant.

The correct answer is (D). This is a conservation of momentum question. Since the momentum before an event must equal the momentum after an event, the momentum must be 12,500 kg·m/s.

The correct answer is (E). The photon of yellow light does not contain enough energy to cause the metal to emit an ultraviolet photon. Remember the energy of a photon is directly related to the frequency of the electromagnetic radiation. The higher the frequency, the higher the energy of the photon of the radiation. Ultraviolet light has a much higher frequency than yellow light, thus its photon is more energetic.

The intensity (power per unit area) is proportional to 1/r2, where r is the distance between the source and the detector. If r increases by a factor of 10, the intensity decreases by a factor of 100. Because the decibel scale is logarithmic, if the intensity decreases by a factor of 100 = 102, the decibel level decreases by 10 log (102) = 20 dB.

The correct answer is (B). Although the person has moved further from the center of the earth, that person now has the additional mass of Mt. Everest under him. i. Point the thumb of the right hand in the direction of the current or the motion of the particle. iii. The palm of the right hand points in the direction of the applied force.

The correct answer is (D). Wavelength has the units meters/wave and frequency has the units waves/second. The product of the two produces a velocity unit

Refraction, the change in the direction of a wave when it enters a new medium, is caused by the change in the speed of the wave as it travels within the new medium.

The correct answer is (E). The father holds the child at the same distance from the ground. If there is displacement, there is no work done.

4 B Use the definition ∆V = -. If an electric field accelerates a negative charge doing positive work on it, then WE > 0. If q < 0, then - is positive. Therefore, ∆V is positive, which implies that V increases.

The strength of the magnetic field at a distance r from a long, straight wire carrying a current I is proportional to I /r; that is, B is inversely proportional to r. So, at the distance from the wire, the magnetic field will be twice as strong.

The strength of the electric field at a point that is a distance r from a point charge of magnitude Q is given by the expression . If the source charge is surrounded by an insulating medium other than vacuum, then the value of k we use in this expression is actually , where k0 is Coulomb's constant and K is the dielectric constant of the medium. The sign of the source charge will affect the direction of the electric field vector at a point but not the strength of the field.

The correct answer is (B). A negative ion is an object that has an excess of electrons. Electrons are the negatively charged part of the atom, therefore they give an object that carries excess of electrons a negative charge.

The correct answer is (B). If there is no unbalanced force applied to an object, the object is not accelerated. An unbalanced force always causes acceleration of the object to which it is applied.

The correct answer is (D). The reactors produce heat, which in turn changes water to steam, which is used to turn the turbines to generate electricity.

The correct answer is (A). The refrigerator is essentially a heat engine that is being run in reverse. The refrigerator heats the room outside by removing heat energy from the enclosed and insulated refrigerator box. The process produces the cooling effect.

The correct answer is (D). The momentum before the explosion must equal the momentum after the explosion. Initially, the momentum of the parts was zero; therefore, all the parts moving in all directions could be added together, and they would equal the momentum before the explosion: zero!

The impulse delivered to the ball is equal to the ball's change in momentum, and the presence of the mitt does not change this, eliminating A and C. The extra area may decrease the pressure on the catcher's hand, but not the force (eliminating B). The padding of the mitt causes the time during which the ball comes to a stop to increase (just as an air bag increases the time it takes for an automobile passenger involved in an accident to come to a stop), which decreases the magnitude of the ball's acceleration (since a = (delta)v/(delta)t). A decrease in the magnitude of the acceleration means a decrease in the magnitude of the force (since a = F/m).

Mass is an intrinsic property of an object and does not change with location. This eliminates A and C. If an object's height above the surface of the earth is equal to 2RE, then its distance from the center of the earth is 3RE. Thus, the object's distance from the earth's center increases by a factor of 3, so its weight decreases by a factor of 32 = 9.

The correct answer is (E). According to the first condition of equilibrium, the sum of all the applied forces must equal zero if an object is not to move.

The correct answer is (A). Electrons in photovoltaic metals are only energized by the photons that carry enough energy to dislodge the electrons.

The speed of a wave is determined by the properties of the medium, not by the frequency. (An exception to this general rule includes light through a transparent material medium such as glass ”the speed depends slightly on the frequency, and this accounts for the phenomenon of dispersion, which can be seen in the familiar spreading of white light into its component colors when it passes through a prism.) Since wave speed is independent of frequency in the situation described here, the answer is C.