A man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depicts the motion of the centre of mass of the entire system (man, the ball and the box)?

In the figure shown find out the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from $O$ in which a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of large circular plate

Give 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 inside the body ?

Three point particles of masses $1.0\; \mathrm{kg} .1 .5 \;\mathrm{kg}$ and $2.5\; kg$ are placed at three comers of a right angle triangle of sides $4.0\; \mathrm{cm}, 3.0 \;\mathrm{cm}$ and $5.0\; \mathrm{cm}$ as shown in the figure. The center of mass of the system is at a point

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

Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are $100\; g , 150 \;g ,$ and $200\; g$ respectively. Each side of the equilateral triangle is $0.5\; m$ long.