Two masses $m_1$ and $m_2$ $(m_1 > m_2)$ are connected by a massless,flexible,and inextensible string passed over a massless and frictionless pulley. The acceleration of the center of mass of the system is

On a smooth horizontal plane,a uniform string of mass $M$ and length $L$ is lying in a state of rest. $A$ man of the same mass $M$ is standing next to one end of the string. Now,the man starts collecting the string. Finally,the man collects all the string and puts it in his pocket. What is the displacement of the man with respect to the Earth in the process of collection?

Two bodies of $6 \,kg$ and $4 \,kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is

$A$ trolley of length $L$ has a pistol fixed on its wall as shown in the figure. The mass of the (trolley + pistol) is $M$. $A$ bullet of mass $m$ is fired from the pistol with a velocity $v_0$ and hits the opposite wall. What is the distance moved by the trolley during the time the bullet travels to hit the opposite wall?

Two particles of masses $2 \ kg$ and $1 \ kg$ are moving along the same line with speeds of $2 \ m/s$ and $5 \ m/s$ respectively. If both particles are moving in the same direction,the speed of the centre of mass is $v_1$. If both particles are moving in opposite directions,the speed of the centre of mass is $v_2$. Find $v_1$ and $v_2$.

Explain translational motion by the given illustration.