The centre of mass of a non uniform rod of length $L$ whose mass per unit length $\lambda $ varies as $\lambda \ =\ \frac{{k\,.\,{x^3}}}{L}$ where $k$ is a constant & $x$ is the distance of any point on rod from its one end, is at distance (from the same end)

A system consists of $3$  particles each of mass $m$ and located at $(1, 1), (2, 2), (3, 3)$. The co-ordinate of the centre of mass are

A projectile of mass $3\,m$ explodes at highest point of its path. It breaks into three equal parts. One part retraces its path, the second one comes to rest. The distance of the third part from the point of projection when it finally lands on the ground is ........$m.$ (The range of the projectile was $100\,\,m$  if no explosion would have taken place)

The $x, y$ coordinates of the centre of mass of a uniform $L-$ shaped lamina of mass $3\, kg$ is

There are some passengers inside $a$ stationary railway compartment. The track is frictionless. The centre of mass of the compartment itself (without the passengers) is $C_1$, while the centre of mass of the 'compartment plus passengers' system is $C_2$. If the passengers move about inside the compartment along the track.

Write the difference between centre of gravity and centre of mass of a body?