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?

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?

A system consists of two particles located at the origin. If one of the particles moves along the x-axis, the centre of mass will:

Two particles of masses 1 kg and 2 kg are located at ${x_1} = 0,\;{y_1} = 0\,and\,{x_2} = 1,\;{y_2} = 0$ respectively. The centre of mass of the system is at

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 ?

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

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

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

Two bodies of mass 10 kg and 2 kg are moving with velocities $\left( {2\hat i - 7\hat j + 3\hat k} \right)\,m/s$ and $\left( { - 10\hat i + 35\hat j - 3\hat k} \right)\,m/s$ respectively. The velocity of their centre of mass is

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

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