**Final Examination
**

Physics 104

15 December 1982
#1. A Certain top having a fixed rate of spin is placed in a
rocket on the earth's surface. With the rocket at rest, the top
precesses with an angular speed of ** 0.15 rev/sec.** The rocket
is then ignited, accelerating straight up, and the top then
precesses at ** 0.45 rev/s.** The acceleration (**in ft/sec**^{2}) of the
rocket is most nearly equal to

**Answer:**

#2. A mass of ** 1.60 kg** undergoes ** SHM** with a period of** 2.00 s ** and
an amplitude of ** 0.250 m**. The maximum resultant force (**in N**)
which must act on the mass is most nearly equal to

**Answer:**

#3. A spring (negligible mass) hangs from the ceiling with a mass
attached to its lower end. The mass is initially held at rest in such a
position that the spring is not stretched. The mass is then released from
this position and oscillates up and down with its lowest position being a
distance **D** below its initial position. The frequency of oscillation
is

**Answer:**

#4. The sketch shows two masses ** M**_{1} and** M**_{2}, which
are uniformly distributed in the shape of cylindrical shells. Mass ** m** is
located within ** M**_{1}. The magnitude of the total gravitational
force acting on m is equal to

**Answer:**

#5. A rocket is accelerated to a speed of **v = Ö(5gR)
**near the earth's surface, where **R** is the radius of the earth.
When it is very far from earth, its speed is equal to

**Answer:**

#6. Two immiscible liquids of densities ** r**_{0}
and ** r**_{x}
are placed in an open U-tube manometer and come into equilibrium as shown in the
sketch. The density ** r**_{x} is equal to

**Answer:**

#7. An object of weight ** W** and density** r ** is held at rest under water (density
**r**_{W} ) by a cord of negligible mass. See sketch. The tension in the
cord is equal to

**Answer:**

#8. A standing wave is set up in a ** 30 cm** long string as shown in the sketch. It vibrates with a frequency of
**60 Hz**. The speed (**in cm/s**) of the wave is most nearly equal to

**Answer:**

#9. A string vibrates in its fundamental mode, making a sound with a
frequency of ** 400 Hz**. A second, identical string produces sound
with the same pitch. The tension in the second string is then increased so
that when both strings are vibrations, a beat frequency of ** 4.0 Hz**
is produced. The fractional increase in the tension force of the second
string is most nearly equal to
**Answer:**

#10. The sound levels in two different cars moving at **35 mph** are compared
at a standard frequency. Car **A** has a level of **60 dB**, while car **B**
has a level of **70 dB**. If the average displacement of sound waves in car **B**
is **y**_{B} and in car **A** is **y**_{A}, then
**y**_{B }/ y_{A} is most nearly equal to
**Answer:**

#11. A test tube is filled with diatomic nitrogen (**28 amu**) gas at
**STP**, and it is made to resonate at its fundamental frequency of
**400 Hz**. A second identical test tube is filled with a gas **"F"**
[**220 amu**] at **STP**, and it is found to resonate at a fundamental frequency
of **140 Hz**. The ratio of specific heats for the gas **"F"** is most nearly
equal to
**Answer:**

#12. A constant volume gas thermometer containing pure oxygen is held at the
**triple point temperature of water**, and it reads a pressure of **75.00 mm of Hg**.
The thermometer is then placed in thermal contact with a liquid until equilibrium is
established and its pressure is found to be **92.00 mm of Hg**. Given the
respective
questions:
- What is the temperature (in
^{o}K) of the liquid?
- Is this the most accurate measurement of that temperature?

the respective **Answers** are:

#13. The temperature of an aluminum disc is increased from **20**^{o}C
to **220**^{o}C, and its area increases by ** 0.92 %.** The coefficient of
linear expansion for aluminum (in ^{o}C^{-1}) is most nearly
equal to

**Answer:**

14. A thermodynamic system is taken from state **A** to
state **B** to state **C** and back to state **A**,
as shown by the path in the ** P-V** diagram. For the process from
**A** to **B**, given that ** U**_{AB} = (+), the
respective values for **Q** and **W** are

**Answer:**

#15. Two metal rods, **A** and **B**, are joined end-to-end. They have
equal cross-sectional areas. The left end or
rod **A** is kept at **100 **^{o}C by contact with boiling water,
while the right end of rod **B** is kept at **0 **^{o}C by contact with an
ice-water mixture. The thermal conductivity of rod **A** is** 3** times
that of **B**, but it is only half as long as **B**. After steady
state conditions have been reached, the temperature ( in ^{o}C)
at the place where the rods are joined is most nearly equal to
**Answer:**

#16. The internal energy (in **cal**) of **one mole** of in ideal monatomic gas
at **STP** is most nearly equal to
**Answer:**

#17. **n moles** of an ideal gas are at a pressure ** p**_{0} and a temperature
**
T**_{0}. It undergoes an adiabatic expansion, doubling its
volume. The work done **by** the gas is equal to

**Answer:**

#18. The ** rms ** speed of molecules is ** correctly** calculated from the
expression
**Answer:**

#19. A refrigerator operates between a low temperature in its interior of **-20 **^{o}C
and a high temperature outside of **30 **^{o}C. In order to remove **1.00 cal** of
heat energy from the inside to the outside of the refrigerator, the minimum amount of energy
(in **cal**) required is most nearly equal to
**Answer:**

#20. Ice has a **heat of fusion** of **80 cal / gm**. If **5.0
gm** of ice is melted at **0 **^{o}C, then the change in **entropy**
(in **cal /**^{o}K) of ice is most nearly equal to

**Answer:**

#21. A beam of light from a laser (wavelength **643.8 nm** in vacuum)
propagates through glass with an index of refraction of **1.50**. The
wavelength (in **nm**) of the laser light in the glass is most nearly
equal to

**Answer:**

#22. A concave, spherical surface of radius **5 cm** separates an air-to-glass
interface. The glass has an index of refraction of **1.50**. An object, **O**,
is placed on the axis, as shown, a distance of **15 cm** to the left of the
interface. Relative to the interface, its image lies

**Answer:**

#23. An object is placed in front of a concave, spherical mirror of radius **r**,
as shown in the sketch. By sketching a ray diagram, one may deduce correctly that the
image is
**Answer:**

#24. For the situation in Problem #23., take the radius of the mirror to be **5 cm**
and the object distance to be **12 cm**. The magnification is then most nearly equal to

#25. A thin lens is made of glass with an index of refraction of **1.50**. The left
side of the lens is flat, and its right side is concave, with a radius of **10 cm**.
See sketch. An object is placed **15 cm** to the left of the lens. Its image is
**Answer:**