A uniform rod of mass $M$ and length $L$ is bent into a semicircular ring. The coordinates of the center of mass of the semicircular ring are:

2 bodies of different masses of 2 kg and 4 kg are moving with velocities 20 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass

If linear density of a rod of length 3 m varies as $\lambda = 2 + x$, then the position of the centre of gravity of the rod is

Two particles of masses $m_1$ and $m_2$ are connected by a light inextensible string passing over a smooth pulley. If the acceleration of the center of mass of the system is $g/4$, what is the ratio of the masses $m_1/m_2$?

Two objects of equal mass are moving towards each other with equal speeds. The velocity of their centre of mass is:

Two particles of masses 2 kg and 4 kg are moving with velocities 4 m/s and 2 m/s respectively along the x-axis. The velocity of the center of mass of the system is:

A system consists of three particles located as follows: $m_1 = 1$ kg at $(0, 1)$, $m_2 = 2$ kg at $(1, 0)$, and $m_3 = 3$ kg at $(1, 1)$. The coordinates of the center of mass are:

An isolated particle of mass m is moving in a horizontal plane (x-y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at $y = + 15$ cm. The larger fragment at the instant is at

A system consists of three particles, each of mass m and located at (1, 1) (2, 2) and (3, 3). The coordinates of the centre of mass are

Two particles of masses 2 kg and 4 kg are moving with velocities 4 m/s and 2 m/s respectively along the same direction. What is the velocity of the centre of mass?

A man of mass M stands at one end of a plank of mass m and length L, lying on a smooth horizontal surface. The man walks to the other end of the plank. The distance moved by the plank with respect to the ground is: