In the figure, two spheres of mass m = 6.52 kg. and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere? M M₁

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You are evaluating a method for studying liquid crystals. Two identical crystals are mounted over the two slits of a double-slit apparatus. The slits are illuminated with monochromatic coherent light and the interference pattern is observed on a screen. An electric voltage is then applied to one of the two crystals, causing its index of refraction to increase and the interference pattern to shift to one side. Your boss has asked you to calculate the change in the index of refraction of the electrified crystal in terms of distance between the two slits, the distance from the slits to the observing screen, the thickness of the crystals, the original index of refraction of the crystals (when not electrified), the wavelength of the light used, and the distance that the central maximum of the pattern is observed to shift when the voltage is applied (you might not use all of these quantities in your answer). two crystals double slits Light observing screen

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