PROBLEM 1 Shown in the picture is the ammonia molecule, NH3. The hydrogens are at the corners of an equilateral triangle, with sides 0.16 nm. This triangle forms the base of a pyramid, with the nitrogen at the apex. The nitrogen lies 0.037 nm vertically above the plane of the triangle. The mass of an H-atom is 1 u, while one N-atom is 14 u. N - Nitrogen H - Hydrogen The center of mass of this molecule lies exactly below the nitrogen. Determine the distance between the center of mass and the nitrogen atom. PROBLEM 2 y Determine the location of the center of mass (xcm, ycm) of the thin semi-circular plate shown in the picture. Assume that the plate has a uniform density and that its radius is equal to R. x PROBLEM 3 Consider the cone shown in the picture. The cone has a uniform density, a height H, k and the circular base has a radius R. Determine the distance between the apex [here ' ' at the origin] and the center of mass. " Hint: ithelps to divide the cone into many thin disks of thickness dz, one of which is shown I 7 in the picture. 1 ' n'"