Aplumb bob consists of a weight hanging from a string. if it hangs without swinging, the string defines the effective direction of gravity. suppose you are holding the bob on the surface of the earth at colatitude e, where e measures the spherical angle as measured from the north pole. (a) in class, we showed that the bob hangs in a direction not exactly toward the center of the earth (assume the earth is a sphere). rather, we defined an 'effective' gravitational acceleration, geff = 9 + 122r sine, where ğ is the gravitational acceleration near the surface of the earth and points directly at the center of the earth, r is the distance from the center of the earth to the point of interest on the surface, where the plumb bob is hanging, 0 is the co-latituted of the plumb bob, and p is the cylindrical unit vector pointing away from the axis of rotation and passing through the surface position of the plumb bob. show that jeff deviates from ğ by an angle r122 sin cos e 9 - rn22 sin? 0 (1) where r is the radius of the earth, n is the earth's angular velocity, and g is the accelerationg due to gravity. (b) where on the earth (i. e., at which colatitude 6) is this angle the largest? what is the maximum value of e? what is its value in boulder?