Two blocks of masses $m$ and $2m$ are placed on a smooth horizontal surface and connected by a spring. If an impulse $J$ is applied to the lighter block, the velocity of the center of mass immediately after the impulse is:

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 non-uniform thin rod of length L is placed along X-axis as such its one of ends is at the origin. The linear mass density of rod is $l = {l_0}x$. The distance of centre of mass of rod from the origin is

A bomb explodes in mid-air into two equal fragments. Which statement is true about the center of mass of the system after the explosion?

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

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

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 bodies of masses 5 kg and 3 kg are moving towards each other with $2\,m{s^{ - 1}}$ and $4\,m{s^{ - 1}}$ respectively. Then velocity of centre of mass 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

When an external force is applied at the centre of mass of a rigid body at rest, then it undergoes

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