1995 Physics Olympiad Screening Test (21-30)

21. You are given two lenses, a converging lens with focal length +10 cm and a diverging lens with focal length - 20 cm. Which of the following would produce a virtual image that is larger than the object?

A. Placing the object 5 cm from the converging lens.
B. Placing the object 15 cm from the converging lens.
C. Placing the object 25 cm from the converging lens.
D. Placing the object 15 cm from the diverging lens.
E. Placing the object 25 cm from the diverging lens.

22. Light shining through two very narrow slits produces an interference maximum at point P when the entire apparatus is in air (see accompanying figure).

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For the interference maximum represented, light through the bottom slit travels one wavelength further than light through the top slit before reaching point P. If the entire apparatus is immersed in water, the angle q to the interference maximum:

A. is unchanged
B. decreases because the frequency decreases.
C. decreases because the wavelength decreases.
D. increases because the frequency increases.
E. increases because the wavelength increases.

23. The magnitude of the field due to an infinite plate of charge is s/(2e_o), where s is the charge per unit area and e_o is the vacuum permittivity. The figure shown below depicts three infinite plates of perpendicular to the plane of the page with charge per unit area + s₁, + 2s₁, and - s₁.

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The total field at the point labeled X is:

A. 4s₁/(2e_o) to the left.
B. s₁/(2e_o) to the left.
C. 0
D. s₁/(2e_o) to the right.
E. 4s₁/(2e_o) to the right.

24. There are three conducting spheres of identical diameter, shown below. Spheres 1 and 2 are separated by a distance that is large compared to their diameter. They have equal charges and repel each other with an electrostatic force F.

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Sphere 3 is initially uncharged and has an insulated handle. It is touched first to sphere 1, then to sphere 2, and then removed. If the distance between spheres 1 and 2 has not changed, the force between these two spheres is:

A. 0
B. ¹/₁₆ F
C. ¹/₄ F
D. ³/₈ F
E. ¹/₂ F

25. Two conducting spheres, A of radius a and B of radius b, are shown in the accompanying figure. Both are positively charged and isolated from their surroundings. They had been connected by a conducting wire but the wire has been removed.

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Assuming the potential an infinite distance away is zero, which of the following statements about the spheres are true:

I. Sphere A is at the higher potential.
II. Sphere B is at the higher potential.
III. Both spheres have the same potential.
IV. Sphere A has the larger charge.
V. Sphere B has the larger charge.
VI. Both spheres have the same charge.

A. I and IV
B. I and VI
C. II and VI
D. III and IV
E. III and V

26. The accompanying figure shows two concentric spherical shells isolated from each other. The smaller shell has radius b and net charge + q. The larger shell has radius B and net charge + Q. Assume that the potential is zero at an infinite distance from the shells.

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If R is the distance from the common center, the highest electric potential V occurs:

A. only at R = 0, where V is infinite.
B. anywhere R Ł b, where V is constant
C. in the region b < R < B.
D. immediately outside the larger shell; V is zero everywhere within it.
E. far away from the shells; V increases with distance.

27. In the circuit represented below, the current I equals:

1995ques27.gif (1659 bytes)

A. ^V/_5R
B. ^V/_4R
C. 2^V/_5R
D. 2^V/_4R
E. 2^V/_R

Use the circuit below to answer questions 28 and 29. L₁, L₂, L₃, and L₄ are identical light bulbs.

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There are six voltmeters connected to the circuit as shown. Assume that the voltmeters do not effect the circuit.

28. Which of the following combinations are equal to V₀?

A. V₁ + V₃
B. V₂ + V₃ + V₄
C. V₁ + V₅
D. V₃ + V₄
E. V₁ + V₄

29. If L₃ were to burn out, opening the circuit, which voltmeter(s) would read zero volts?

A. None would read zero.
B. only V₃
C. only V₄
D. only V₃, V₄, and V₅
E. they would all read zero

30. Identical currents flow in two perpendicular wires, as shown in the accompanying figure. The wires are very close but do not touch.

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The magnetic field can be zero:

A. at a point in region 1 only
B. at a point in region 2 only
C. at points in both regions 1 and 2
D. at points in both regions 1 and 4
E. at points in both regions 2 and 4