A particle of mass $m$ moves along a trajectory given by $\vec{r}(t) = (t - \sin(t))\hat{i} + (1 - \cos(t))\hat{j}$, where $t$ is time. The net force acting on the particle 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 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

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

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

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?

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:

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

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