Two bodies of masses $m_1$ and $m_2$ are connected by a massless string passing over a massless,frictionless pulley as shown in the figure. Given $m_2 < m_1$. The acceleration of the center of mass of the system is:

Discuss the explosion of a projectile.

The equation $M\vec{A} = \vec{F}_{ext}$ denotes what?

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Two bodies of masses $12 \,kg$ and $6 \,kg$ are projected simultaneously with velocities $15 \,ms^{-1}$ and $20 \,ms^{-1}$ respectively from the top of a tower of height $25 \,m$. The body of mass $12 \,kg$ is projected vertically upwards and the body of mass $6 \,kg$ is projected horizontally. Find the maximum height reached by the centre of mass of the system of two bodies from the ground. $(g = 10 \,ms^{-2})$ (in $\,m$)

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration $\vec{f}$. The centre of mass has an acceleration