Motion of the Centre of Mass

A juggler juggles three balls in a continuous cycle. Any one ball is in contact with his hand for one-fifth of the time. Describe the motion of the centre of mass of the three balls. What average force does the juggler exert on one ball while he is touching it?

In a certain (2/5) th of the energy of molecules is associated with the ratation of molecules and the rest of it is associated with the motion of the centre of mass. (a) What is the average translational energy of one such molecule when the temperature id 27^@ C ? (b) How much energy must be supplied to one mole of thsi gas constant volume to raise the temperature by 1^@ C ?

Figure (a) and (b) shows two different arrangements of a spool being pulled with a constant force F in each case. Identify the direction of motion of the centre of mass, and the direction of friction force in each case. a. The CM moves along………………. x -axis . b. The friction force acts along…………………. x -axis. c. The CM moves along ..... x -axis. d. The friction force acts along…………….. x -axis.

The position of the centre of mass of a cube of uniform mass density will be at

What is the location of the centre of mass of a uniform triangular lamina ?

Given the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie on the body ?

A uniform straight rod is placed in vertical position on a smooth horizontal surface and released. As the rod is in motion, the centre of mass moves

The position co-ordinates of the centre of mass of a system of three particles of equal masses which are placed on the verctices of an equilateral triangle of a side a are shown. Locate centre mass?

Five masses are placed in a plane as shown in figure. The coordinates of the centre of mass are nearest to

The co-ordinates of the centre of mass of the system as shown in figure are