A circle is made by bending a rod having a uniform mass distribution. It's then cut in half along the diameter. If the radius of the circle was r, find the center of mass of the semicircle for a coordinate system that has its origin at the center of the circle.

Calculate the distance from the nitrogen atom to the center of mass of a nitrogen monoxide (NO) molecule, where the nitrogen atom (m = 14 u) and the oxygen atom (m = 16 u) are separated by 1.14 x 10⁻¹⁰ m.

Determine the position of the center of mass of a circular table, relative to the center of the table, weighing 7.1 kg and having a radius of 35 cm, which is unbalanced due to a 1.51-kg decorative piece placed 25 cm from the table's center.

Consider a 1251-kg unoccupied van. Initially, the center of mass of the van is located 2.41 m behind the front. Now, consider the scenario where one individual is seated in the front seat, positioned 2.81 m from the front, and two individuals are seated in the back seat, which is located 3.91 m from the front. Determine the distance of the new center of mass from the front of the van. Assume each person weighs 66 kg.

Determine the distance from the Jupiter-Ganymede system's center of mass to Jupiter, given that Jupiter has a mass of 1.90 x 10²⁷ kg and Ganymede has a mass of 1.48 x 10²³ kg, with their centers separated by 1.07 x 10⁶ m.