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:

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 uniform rod of mass M and length L is pivoted at one end and rotates with angular velocity ω. The linear velocity of its center of mass 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 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, each of mass m and located at (1, 1) (2, 2) and (3, 3). The coordinates of the centre of mass are

The centre of mass of three particles of masses 1 kg, 2kg and 3kg is at (2, 2, 2). The position of the fourth mass of 4 kg to be places in the system as that the new centre of mass is at (0, 0, 0) 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 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:

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

Four bodies of masses 2, 3, 5 and 8kg are placed at the four corners of a square of side 2m. The position of C.M. will be