Set of miscellaneous problems

Question 1: Two people stand 3.0 m away from a large plane mirror and are 5.0 m apart from each other in a dark room. At what angle of incidence should one of them shine a flashlight on the mirror so that the reflected beam strikes the other person at the same height that the flashlight is held? Assume the person with the flashlight holds it near his body?

Question 2: Two plane mirrors, M1 and M2, are placed together as illustrated in the figure(see attachment)

a. If the angle between the mirrors is 70 degree and the angle of incidence of a light ray incident on M1 is 35 degree, what is the angle of reflection from M2?

b. If the angle between the mirrors is 115 degree and the angle of incidence of a light ray incident on M1 is 60 degree, what is the angle of reflection from M2?

Question 3: The laser used in cornea surgery to treat corneal disease is the excimer laser, which emits ultraviolet light with a wavelength of 193 nm in air. The index of refraction of the cornea is 1.376. What are the wavelength and frequency of the light in the cornea?

Question 4: A cube of flint glass sits on a newspaper on a table. By looking into one of the vertical sides of the cube, is it possible to see the portion of the newspaper covered by the glass?

Question 5: A beam of light with red and blue components of wavelengths 670 nm and 425 nm, respectively, strikes a slab of fused quartz at an incident angle of 30 degree. On refraction, the different components are separated by an angle of 1.31 X 10^-3 rad. If the index of refraction of the red light is 1.4925, what is the index of refraction of the blue light?

Question 6: An opaque container is 15 cm deep. It contains only a single coin. When looking into the container at a viewing angle of 50 degree relative to the vertical side of the container, you see nothing on the bottom. When the container is filled with water, you see the coin (from the same viewing angle) on the bottom of, and just beyond, the side of the container. How far is the coin from the side of the container?

Question 7: If a certain amount of gas fills a 1 liter container and exerts a pressure on the walls of 2.0 N/m^2 at 20 degree C, what would the pressure theoretically be at absolutely zero. Assume it is ideal gas and the container size remains constant.

A. 0.025 N/m^2
B. Cannot tell because need to know the amount of gas.
C. Cannot tell because need to know what the gas is.
D. 0.050 N/m^2
E. 0.0037 N/m^2

Question 8: The center of mass of an object must always be located where the physical material of the object located?

A. True
B. False

Question 9: A golf ball traveling at 3 m/s to the right has a head on collision with a stationary bowling ball in a friction free environment. If the collision is almost perfectly elastic, the speed of the golf ball immediately after the collision is:

A. Slightly less than 3 m/s
B. Equal to 3 m/s
C. Slightly greater than 3 m/s
D. Much less than 3 m/s

Question 10: The moon pulls on the earth with 1/6 the force that the earth exerts on the moon.

A. True
B. False

Question 11: Which temperature is higher, 300 degree F or 400 K?

A. 300 degree F
B. 400 K

Question 12: If the distance to a sound source is halved, how will the sound intensity level change?

A. Depends on the actual distance
B. Increase by 3 db
C. Increase by 6 db
D. Increase by a factor of 4
E. Increase by a factor of 2

Question 13: Is it possible for a system to have a negative potential energy.

A. Yes, as long as the total energy is positive
B. Yes, since the choice of the zero potential energy is arbitrary
C. No, because the kinetic energy of a system must equal its potential energy
D. No, because this would have no physical meaning.

Question 14: Assuming the water molecules in the gas phase act as an ideal gas, how many times greater in the rms speed of water molecules in the gas phase at the boiling temperature of water compared to the freezing temperature of water?

A. You cannot divide by zero
B. 5.000 times as fast
C. 2.236 times as fast
D. 1.169 times as fast
E. 1.366 times as fast

Question 15: Two identical masses are attached by a light string that passes over a small pulley. One of the masses rest on a flat table top while the other hangs over the edge (assume this mass does not touch the ground). The table and pulley are frictionless. The masses are moving:

A. at constant speed
B. with an acceleration equal to g
C. with an acceleration less than g
D. with an acceleration greater than g

Question 16: A 100 kg football linebacker moving at 2 m/s tackles head-on an 80 kg halfback running 3 m/s. Assume the two players were initially running directly at one another. Neglecting the effects due to digging in of the cleats:

A. this is simple example of elastic collision.
B. The halfback will drive the linebacker backwards
C. The linebacker will drive the halfback backwards
D. Neither player will drive the other backwards

Question 17: An ice cube floats in a glass of water. As the ice melts, the level in the glass will:

A. Increase
B. Decrease
C. Stay the same

Question 18: Kinetic energy is linearly proportional to speed.

A. True
B. False

Question 19: A 42.0 Kg block of ice slides down a plane with an incline of 34 degree.
Assuming the friction is negligible, what is the acceleration of the block down the incline?

A. 5.48 m/s^2
B. 9.80 m/s^2
C. 8.12 m/s^2
D. 6.61 m/s^2

Question 20: Consider two slabs of material with the same thickness, but made of material differing in their index of refraction. Which of the following is true?

A. Light incident at an angle from normal will reflect of two slabs at different angles'
B. The wavelength of the light will be the same in the two slabs.
C. The frequency of light will differ in the two slabs
D. Light incident normally will reflect at different angles in the two slabs
E. The speed of light will differ in the two slabs

Question 21: If two identical masses are attached by light cord which is passing over mass-less, frictionless pulley of an Atwood's machine, but at different heights, and released.

A. the higher mass will go down
B. the masses will not move
C. the motion will depend on the amount of the masses
D. the lower mass will go down

Question 22: Two dams form artificial lakes of equal depth. However, one lake back up 15km behind the dam, and the other back up 30km behind. What effects does the difference in the length have on the pressure of the dams?

See attached file for full problem description with diagrams.