1996 Physics Olympiad Screening Test (1-20)

1. An object is projected straight upward from ground level with a velocity of 50 m/s. Ignoring air resistance, it will return to ground level in approximately:

A. 2.5 s
B. 5.0 s
C. 7.5 s
D. 10 s
E. 15 s

2. A jogger runs with constant speed v through a forest of pine trees. A pine cone starts to fall from a height h when the jogger is directly below it. How far behind the jogger will the pine cone land?

3. A ball is thrown downward with speed 15 m/s from the roof of a 30 m building. At the same instant a ball is thrown upward with speed 15 m/s from ground level. Relative to ground level, the two balls pass each other at a height of:

A. 0
B. 5.0 m
C. 10 m
D. 15 m
E. 20 m

4. A swimmer can swim with a velocity of 1.0 m/s in still water. The swimmer wishes to swim directly across a river with a current of 0.50 m/s directed from upstream to downstream. To end up directly across the river the swimmer must head at an angle of:

A. tan^-1 (½) upstream.
B. sin^-1 (½) upstream.
C. directly across the river.
D. sin^-1 (½) downstream
E. tan^-1 (½) downstream

5. What is the tension T in the rope if the 10-N weight is moving upward with constant velocity?

PO1996ques5diagram.gif (1714 bytes)

A. 3.5 N
B. 5.0 N
C. 7.1 N
D. 10 N
E. 14 N

6. As shown, two blocks with masses m and M (M > m) are pushed by a force F in both Case I and Case II. The surface is horizontal and frictionless. Let R_I be the force that m exerts on M in case I and R_II be the force that m exerts on M in case II.

PO1996ques6diagram.gif (1891 bytes)

Which of the following statements is true?

A. R_I = R_II = 0
B. R_I = R_II and is not equal to zero or F.
C. R_I = R_II = F
D. R_I < R_II
E. R_I > R_II

7. Two blocks, with masses 17 kg and 15 kg, are connected by a light string that passes over a frictionless pulley of negligible mass as shown. The surfaces of the planes are frictionless. The blocks are released from rest. T₁ and T₂ are the tensions in the strings.

PO1996ques7diagram.gif (2142 bytes)

Which of the following statements is correct?

A. The 15-kg block accelerates down the plane.
B. The 17-kg block accelerates down the plane.
C. Both blocks remain at rest.
D. T₁ > T₂
E. T₁ < T₂

8. A small block of mass m starts from rest at the top of a globe of radius R.

PO1996ques8diagram.gif (1818 bytes)

At what angle q does it slide off the surface of the globe? Assume the system is frictionless.

A. q = 0º
B. q = cos^-1 (¹/₃)
C. q = cos^-1 (²/₃)
D. q = 60º
E. q = 90º

9. An object with mass m and initial velocity v is brought to rest by a constant force F acting for a time t and through a distance d. Possible expressions for the magnitude of the force F are:

I. (mv²) /( 2d)
II. (2md) / t²
III. (mv) / t

Which of these give(s) the correct expression for the magnitude of the force F?

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III

10. A small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.

I – kinetic energy
II – potential energy
III – momentum

Which of these quantities will change as this sphere moves around the circle?

A. I and II only
B. I and III only
C. II only
D. III only
E. II and III only

11. A roller coaster travels with speed v_A at point A. Point B is a height H above point A. Assuming no frictional losses and no work done by a motor, what is the speed at point B?

12. Three air track cars are initially placed as shown in the accompanying figure. Car A has mass m and initial velocity v to the right. Car B with mass m and car C with mass 4m are both initially at rest. Car A collides elastically with car B, which in turn collides elastically with car C. After the collision, car B is at rest.

The final velocities of cars A and C are:

A. Car A: 0.6v to the left Car C: 0.4v to the right
B. Car A: 2.6v to the left Car C: 0.4v to the right
C. Car A: at rest Car C: 0.5v to the right
D. Car A: at rest Car C: 0.25v to the right
E. Car A: at rest Car C: v to the right

13. A child with mass m is standing at the edge of a playground merry-go-round with moment of inertia I, radius R, and initial angular velocity w . The child jumps off the edge of the merry-go-round with tangential velocity v with respect to the ground.

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The new angular velocity of the merry-go-round is:

PO1996ques13ans.gif (2992 bytes)

14. As shown, a spool has outer radius R and axle radius r. A string is wrapped around the axle of the spool and can be pulled in any of the directions labeled by I, II, or III.

PO1996ques14diagram.gif (2018 bytes)

The spool will slide to the right without rolling on the horizontal surface if it is pulled in direction(s):

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

15. A uniform flag pole of length L and mass M is pivoted on the ground with a frictionless hinge. The flag pole makes an angle q with the horizontal. The moment of inertia of the flag pole about one end is ¹/₃ ML².

PO1996ques15diagram.gif (1675 bytes)

If it starts falling from the position shown in the accompanying diagram, the linear acceleration of the free end of the flag pole – labeled P – would be:

A. ²/₃ g cos q
B. ²/₃ g
C. g
D. ³/₂ g cos q
E. ³/₂ g

16. The root mean square velocity of oxygen gas (atomic mass 16) is v at room temperature. What is the root mean square velocity of helium (atomic mass 4) at the same temperature?

A. 4 v
B. 2 v
C. v
D. v/2
E. v/4

17. Which of the accompanying PV diagrams best represents an adiabatic process (process where no heat enters or leaves the system)?

PO1996ques17ans.gif (2706 bytes)

18. String A and String B have the same mass and length. String A is under tension T and string B is under tension 2T. The speed of waves in B is _____ times the speed of waves in A.

A. 0.50
B. 0.71
C. 1.00
D. 1.4
E. 2.0

19. On a day when the velocity of sound in air is v, a whistle moves with velocity u toward a stationary wall. The whistle emits sound with frequency f.

PO1996ques19diagram.gif (1300 bytes)

What frequency of reflected sound will be heard by an observer traveling along with the whistle?

PO1996ques19ans.gif (2187 bytes)

20. 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 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.