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School of Science and Engineering Al Akhawayn University Test # 1 Phy1402, Fall 2002 Instructor: Dr. H. Darhmaoui Date: October 18, 2002 1) A student holds a tuning fork oscillating at 256 Hz. He walks towards a wall at a constant speed of 1.33 m/s. (Assume that the speed of sound in air is 344 m/s) (a) What beat frequency does he observe between the tuning fork and its echo? (b) How fast must he walk away from the wall to observe a beat frequency of 5Hz? 2) Two small spheres each of mass m = 2.00 g are suspended by light strings 10.0 cm in length (Figure 1). A uniform electric field is applied in the x direction. If the spheres have charges equal to -5.00 10-8 C and +5.00 108 C, determine the electric field that enables the spheres to be in equilibrium at an angle θ = 10°. Figure 1 3) On planet Tehar, the gravitational field strength is the same as that on Earth (g = 9.81 m/s2) but on Tehar there is also a strong downward electric field that is uniform close to the planet’s surface. A 2.00-kg ball carrying a charge of 5.00 µC is thrown upward at 20.1 m/s and hits the ground after 4.10 s. What is the potential difference between the starting point and the top point of the trajectory? 4) Two hollow conducting spheres have a common center (Figure 2). The dimensions of the spheres are: Sphere 1: inner radius Ra= 0.30 m, outer radius Rb= 0.32 m Sphere 2: inner radius Rc= 0.89 m, outer radius Rd= 0.91 m A charge of –100 nC is placed on the inner conductor and a charge of +60 nC is placed on the outer conductor. a) Find the charges on the inner and outer surfaces of both spheres b) Find the electric field at the following positions: r =0.25 m, 0.31 m, 0.40 m, 0.90 m and 0.95 m. Figure 2 rc ra rb rd Solution