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/sec2) of the rocket is most nearly equal to
Answer:

a) 11     b) 16    c) 32     d) 64     e) 96

#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:

a) l5.7     b) 0.100     c) 2.47     d) 0.25     e) 3.95

#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:

a) 2p Ö(D/g)
b) 1 /(2p) Ö(g/D)
c) 1 /(2p) Ö(2g/D
d) 2p Ö(2g/D)
e) 1 /(2p) Ö(g/2D)

#4.  The sketch shows two masses M1 and M2, which are uniformly distributed in the shape of cylindrical shells.  Mass m is located within M1.  The magnitude of the total gravitational force acting on m is equal to

Answer:
a) GM1m/(r1)2
b) GM2m/(R2)2
c) GM2m/(r1)2 + GM2m/(R2)2
d) GM2m/(R1+R2)2
e) GM2m/(R1+R2)2 + GM1m/(r1-R1)2

#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:
a) Ö(3gR) b)Ö(2gR) c)1/2 Ö(5gR) d)2 Ö(gR) e)Ö(5gR/2)

#6.  Two immiscible liquids of densities r0 and rx are placed in an open U-tube manometer and come into equilibrium as shown in the sketch.  The density rx is equal to

Answer:
a) r0 h1/(h3 - h2)
b) r0(h1 + h2)/h3
c) r0 (h3 - h2)/h1
d) r0 h3/(h1 + h2)
e) r0 h3/h2

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

Answer:
a) W r/rW
b) W rW/r
c) W r/(rW - r)
d) W (1 - r/rW)
e) W (rW/r -1)

#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:
a) 1800    b) 2.0    c) 1200   d) 900  e) 720

#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:

a) 0.010    b) 0.005    c) 0.020   d) 0.025   e) 0.015

#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 yB and in car A is yA, then yB / yA is most nearly equal to

Answer:

a) 3.2    b) 1.2    c) 1.1   d) 1.0   e) 10.

#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:

a) 2.37    b) 1.35    c) 1.40   d) 1.67   e) 1.28

#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 oK) of the liquid?
• Is this the most accurate measurement of that temperature?
the respective Answers are:
a) 222.68 oK; Yes   b) 222.68 oK; No   c) 335.08 oK; Yes   d) 335.08 oK; No   e) 273.16 oK; Yes

#13. The temperature of an aluminum disc is increased from 20oC to 220oC, and its area increases by 0.92 %. The coefficient of linear expansion for aluminum (in oC-1) is most nearly equal to
Answer:
a) 4.6 ´ 10-5    b) 9.2 ´ 10-5    c) 1.2 ´ 10-5   d) 2.3 ´ 10-5  e) 6.9 ´ 10-5

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 UAB = (+), the respective values for Q and W are

Answer:
a) (+), (+)    b) (-), (-)    c) (0), (+)    d) (+), (-)    e) (+), (0)

#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 oC by contact with boiling water, while the right end of rod B is kept at 0 oC 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 oC) at the place where the rods are joined is most nearly equal to

Answer:

a) 33    b) 67    c) 86    d) 50    e) 17

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

Answer:

a) 546    b) 3400    c) 820    d) 2300    e) zero

#17. n moles of an ideal gas are at a pressure p0 and a temperature T0.  It undergoes an adiabatic expansion, doubling its volume.  The work done by the gas is equal to
Answer:
a) n cp T0 (2g -1)
b) n cV T0 (1 - 0.5g-1)
c) n cV T0 (2g-1 -1)
d) n cV T0 (0.5g -1)
e) zero

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

Answer:

a) 1/N ò0¥ [dN/dv] dv
b) 1/N ò0¥ [dN/dV] (Öv) dv
c) 1/N ò0¥ [dN/dv] v dv
d) {1/N ò0¥ [dN/dv] v2 dv}1/2
e) 1/N ò0¥ { [dN/dV] v2 }1/2 dv

#19. A refrigerator operates between a low temperature in its interior of -20 oC and a high temperature outside of 30 oC. 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:

a) 7.3    b) 0.77    c) 0.20    d) 1.77    e) 1.00

#20.  Ice has a heat of fusion of 80 cal / gm.  If 5.0 gm of ice is melted at 0 oC, then the change in entropy (in cal /oK) of ice is most nearly equal to
Answer:
a) -1.46    b) 400    c) 0.059    d) 1.46    e) zero

#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:
a) 965.7    b) 643.8    c) 321.9    d) 1287.6    e) 429.2

#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:
a) 20 cm to the right    b) 20 cm to the left    c) 9 cm to the right    d) 9 cm to the left    e) 6 cm to the right

#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:
a) virtual inverted, reduced    b) real inverted, enlarged    c) virtual erect, reduced
d) real erect, enlarged    e) real inverted, reduced

#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
a) virtual inverted, reduced    b) real inverted, enlarged    c) virtual erect, reduced
d) real erect, enlarged    e) real inverted, reduced

#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:
a) real, 10 cm to the right    b) virtual, 60 cm to the left    c) virtual, 8.6 cm to the left
d) real, 8.6 cm to the right    e) real, 10 cm to the right