A cannon shell, moving along a straight-line, bursts into two parts. Just after the burst, one part moves with momentum $40 \mathrm{N} \mathrm{s}$, making an angle $30°$ with the original line of motion. The minimum momentum of the other part of the shell just after the burst is,

  

A man and a plank of the same mass are moving together with a velocity $v$ along the positive $x$-axis. At some instant of time, the man jumps along the negative axis with a velocity $v$ with respect to ground. Then, the speed of the plank after the jump is,

Two small spheres of equal mass are heading towards each other with equal speeds, undergo a head-on collision (no external force acts on the system of two spheres). Then which of the following statement is correct?

Two masses $\mathrm{m}$ and $2\mathrm{m}$ are placed in a fixed horizontal circular smooth hollow tube as shown. The mass $\mathrm{m}$ is moving with speed $\mathrm{u}$ and the mass $2\mathrm{m}$ is stationary. After their first collision, the time elapsed for next collision is (Coefficient of restitution is, $\mathrm{e}=\frac{1}{2}$)

A particle $A$ moves with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ in a frictionless circular fixed horizontal pipe of radius $5 \mathrm{m}$ and strikes the particle $B$ of double the mass that of $A$. The coefficient of restitution is $\frac{1}{2}$ and the particle $A$ starts its journey at $t=0$. The time at which the second collision occurs is