Two spheres of masses $2M$ and $M$ are initially at rest at a distance $R$ apart. Due to mutual force of attraction,they approach each other. When they are at a separation $R/2$,the acceleration of the centre of mass of the system would be ....... $m/s^2$.

When a bomb explodes during projectile motion,which forces do not contribute to the motion of the centre of mass?

State Newton's second law for a system of particles.

Choose the correct statement$(s)$:
$(A)$ The position of the centre of mass of a system is dependent on the choice of coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.

Internal forces acting within a system of particles can alter

If a force $10 \hat{i} + 15 \hat{j} + 25 \hat{k}$ acts on a system and gives an acceleration $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ to the centre of mass of the system,the mass of the system is