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 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

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 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

If a bomb explodes in mid-air, the center of mass of the fragments:

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 objects of equal mass are moving towards each other with equal speeds. The velocity of their 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 $m_1/m_2$?

Circular hole of radius 1 cm is cut off from a disc of radius 6 cm. The centre of hole is 3 m from the centre of the disc. The position of centre of mass of the remaining disc from the centre of disc is

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

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