An apparatus like the one Cavendish used to find G has large lead balls that are 7.2 kg in mass and small ones that are 0.053 kg. The center of a large ball is separated by 0.063 m from the center of a small ball. Mirror m Light source M r κ The Cavendish apparatus for measuring G. As the small spheres of mass m are attracted to the large spheres of mass M, the rod between the two small spheres rotates through a small angle. Find the magnitude of the gravitational force between the masses if the value of the universal gravitational constant is 6.67259 × 10−11 N m2 /kg2 . Answer in units of N.

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?