CENTER OF MASS

Motion of Mass Center in One Dimension A jeep of mass 2400kg is moving along a straight stretch of road at 80km/h. It is followed by a car of mass 1600 kg moving at 60 km/h. (a) How fast is the center of mass of the two cars moving? (b) FInd velocities of both the vehicles in centroidal frame.

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the figure. If the center of hole is at a distance c from the center of the disc, the distance x_(2) of the center of mass of the remaining part from the initial center of mass O is given by

A mass is at the center of a square, with four masses at the corners as shown. Rank the choices according to the magnitude of the gravitational force on the center mass.

A uniform rod of mass M and length L lies on a frictionless horizontal plane. A particle of same mass M moving with speed v_(0) perpendicular to the length of the rod strikes the end of the rod and sticks to it. Find the velocity of the center of mass and the angular velocity about the center of mass of (rod + particle) system.

Mass Center of a sector of a uniform circular plate Find location of mass center of a sector of a thin uniform plate.

A marble and a cube are placed at the top of a ramp. Starting from rest at the same height, the marble rolls and the cube slides (no kinetic friction) down the ramp. Determine the ratio of the center-of-mass speed of the cube to the center-of-mass speed of the marble at the bottom of the ramp.

A marble and a cube are placed at the top of a ramp. Starting from rest at the same height, the marble rolls and the cube slides (no kinetic friction) down the ramp. Determine the ratio of the center-of-mass speed of the cube to the center-of-mass speed of the marble at the bottom of the ramp.

Mass center of a system of a segment of a uniform circular rod(arc) Find location of mass center of a thin uniform rod bent into shape of an arc.