A system consists of three particles of masses 1 kg, 2 kg, and 3 kg located at the vertices of an equilateral triangle of side $L$. If the 1 kg mass is removed, by what distance does the center of mass of the system shift?

A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The center of mass of the new disc is $\frac{\alpha }{R}\;$ from the center of the bigger disc the value of $\alpha$ is

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

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

A dog of mass $m$ stands at one end of a flat boat of mass $M$ and length $L$ at rest on a frictionless surface of a lake. The dog walks to the other end of the boat and stops. The displacement of the center of mass of the boat-dog system is:

Three masses of 2 kg,4 kg and 4 kg are placed at the three points (1,0,0),(1,1,0) and (0,1,0) respectively. The position vector of its centre of mass 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 $m_1/m_2$?

A cannon shell lands 2 km away from the cannon. A second shell, fired identically, breaks into two equal parts at the highest point. One part falls vertically. How far from the cannon will the other land ?

For an isolated system, the velocity of the centre of mass:

Two masses ${m_1}\,and\,{m_2}$ \left( {{m_1} > {m_2}} \right) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is