The force-time $(F -t) $ curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to $8$ second will be  ........... $N-s$

A particle of mass $m$, initially at rest, is acted on by a force $F = F_0 \left\{ {1 - {{\left( {\frac{{2t - T}}{T}} \right)}^2}} \right\}$ during the interval $0 \leq 0 \leq t \leq T$. The velocity of the particle at the end of the interval is :

A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of body $A$ relative to $B$ is:

Both the blocks shown here are of mass $m$ and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity. The tension in the string connecting both of them will be (Neglect friction)

What should be the minimum force $P$ to be applied to the string so that block of mass $m$ just begins to move up the frictionless plane.