# Topic Category: CENTRE OF MASS AND VRIABLE MASS SYSTEMS

## Problems on Variable Mass Systems

Example 1 :A flat car of mass starts moving to the right due to a constant horizontal force F. Sand spills on the flat car from a stationary hopper. The rate of loading is constant and equal to µ kg/s. Find the time dependence of the velocity and the acceleration of the flat car in …

## Problems on Centre of Mass

Example 1 :A cubical block of ice of mass m and edge L is placed in a large tray of mass M. If the ice melts, how far does the centre of mass of the system “ice plus tray” come down?Solution :Suppose the centre of mass of the tray is a distance above the origin …

## Centre of Mass of Semi ring and Semi Disc

C.M. of Semicircular RINGSuppose mass of semi circular ring is M and radius is R.Mass per unit length Coordinate of Suppose mass of semi disc is M and radius is RSurface mass density, From the symmetry of mass distribution,

## Centre of Mass and Symmetry

Let us discuss the types of symmetry found in nature.Inversion SymmetryA system is said to possess inversion symmetry if there exist a point (called inversion centre) such that if we draw any vector then whatever environment exists at the tip of vector, the same environment prevails at the tip of vector. For example : Sphere …

## Equation of Motion of Centre of Mass

Consider a system of n particles having masses respectively and whose positions are described by vectors respectively.Equation of motion of individual particles are given as …(1) …(2) …(3) ….(i) …(n) If you are interested in motion of individual particles, then you need to solve each equation seperately. If you are interested in motion of system …

## Centre of Mass

Many a times, when we study system of particles, we are not interested in motion of individual particles but motion of system as a whole. In such a situation, centre of mass is useful. Centre of mass is nothing but a weighted mean of position of particles. Let us first understand weighted mean. What is …