ANswer with Details PLZ .. Thank you.. With vector calculus it is simple exercis
ID: 2116701 • Letter: A
Question
ANswer with Details PLZ .. Thank you..
With vector calculus it is simple exercise to show that for a uniformly dense spherical mass (density rho) the magnitude of the acceleration due to gravity inside the sphere is given by where r is the distance from the center of the sphere. Consider the Earth as just such a sphere with a total mass ME = 5.98 times 1024 kg and radius RE = 6.37 times 106 m (The volume of a sphere is given by V = 4 / 3 pi r 3.) A narrow hole is drilled through the Earth on a diameter. Determine the equilibrium location for a small mass m moving in the hole. Write down the form of the force and potential energy on m if it is displaced from equilibrium an amount r. Identify the type of motion that will result. Determine the characteristic time for this motion. Suppose the mass of the Earth were doubled but the radius remained the same. Qualitatively, how would this affect the motion?Explanation / Answer
a) eqm point is the centre of earth... b) force = Gpmx/3 ...PE = -Gpmx^2/6 c) SHM motion as acc. is prop to disp. T = 2pi*sqrt(Gpm/3) d) same motion ...no change