1994 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 real image that is smaller 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. A source at rest emits waves with wavelength l in a medium with velocity v. If the source moves to the right with velocity v_s, the distance between adjacent crests l’ directly behind the source is:

PO1994ques22diagram.gif (1491 bytes)

23. Two sources, in phase and a distance d apart, each emit a wave of wavelength l. See accompanying figure. Which of the choices for the path difference DL = L₁ – L₂ will always produce constructive interference at point P?

PO1994ques23diagram.gif (1939 bytes)

A. d sinq
B. x/L₁
C. (x/L₂)d
D. ½ l
E. 2 l

Questions 24 and 25 are based on the following description: Two point charges of +4.00 mC and –9.00 mC are placed 1.00 m apart, as shown in the accompanying figure. Assume the potential goes to zero as R goes to infinity.

24. The total electric field due to the two charges is zero at a point:

A. 3.00 m to the right of the –9.00 mC charge.
B. 0.40 m to the right of the +4.00 mC charge.
C. 0.31 m to the right of the +4.00 mC charge.
D. 0.80 m to the left of the +4.00 mC charge.
E. 2.00 m to the left of the +4.00 mC charge.

25. How much work is done moving the –9.00 mC charge from its original position to a new position 2.00 m from the +4.00 mC charge?

A. – 0.324 J
B. –0.081 J
C. +0.162 J
D. +0.243 J
E. +0.486 J

26. A point charge Q is placed at the center of a spherical conducting shell, the shaded part of the accompanying figure. A total charge of –q is placed on the shell.

PO1994ques26diagram.gif (2009 bytes)

The magnitude of the electric field at point P₁ a distance R₁ from the center is _____. The magnitude of the electric field at point P₂ a distance R₂ from the center is _____.

PO1994ques26ans.gif (2682 bytes)

27. R₄, as shown in the figure, is a variable resistor.

PO1994ques27diagram.gif (1999 bytes)

In order for there to be no current through the ammeter, R₄ must be equal to:

A. R₂
B. R₃
C. R₁R₂/R₃
D. R₁R₃/R₂
E. R₂R₃/R₁

28. A resistor R dissipates power P when connected directly to a voltage source V, as shown in the accompanying figures.

PO1994ques28diagram.gif (1823 bytes)

What resistance R' must be connected in series with R to decrease the power dissipated in R to ½P?

29. The infinitely long straight wire carries a conventional current I as shown in the accompanying figure. The rectangular loop carries a conventional current I' in the counterclockwise direction.

PO1994ques29diagram.gif (1774 bytes)

The net force on the rectangular loop is:

PO1994ques29ans.gif (4361 bytes)

30. A spatially uniform magnetic field of 0.080 T is directed into the plane of the page and perpendicular to it, as shown in the accompanying figure. A wire loop in the plane of the page has constant area 0.010 m² . The magnitude of the magnetic field decreases at a constant rate of 3.0 x 10^–4 T/s.

PO1994ques30diagram.gif (1611 bytes)

What is the magnitude and direction of the induced emf?

A. 3.0 x 10 ^–6 V clockwise
B. 3.0 x 10 ^–6 V counterclockwise
C. 2.4 x 10 ^–5 V counterclockwise
D. 8.0 x 10 ^–4 V counterclockwise
E. 8.0 x 10 ^–4 V clockwise