A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and $8$ second is
$ - 2\pi \,newton \times second$
$Zero\;newton \times second$
$ + 4\pi \,newton \times second$
$ - 6\pi \,newton \times second$
A particle is moving with a constant speed along a straight line path. A force is not required to
A particle is acted upon by a force whose component's variations with time are shown in diagrams. Then the magnitude of change in momentum of the particle in $0.1\,\,sec$ will be :-
In an hour-glass approximately $100$ grains of sand fall per second (starting from rest); and it takes $2 \, s$ for each sand particle to reach the bottom of the hour-glass. If the average mass of each sand particle is $0.2 \,g$, then the average force exerted by the falling sand on the bottom of the hour-glass is close to .......... $N$
A $40\ g$ ball dropped from a certain height bounces back from the horizontal ground without losing mechanical energy. If its speed is $10\ m/s$ just before making contact with the ground, and the average value of the force of the ground on the ball is equal to $16\ N$ while ball and wall are in contact, how long were they in contact .......... $m/s$
A body of $2\, kg$ has an initial speed $5ms^{-1}$. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body. .......... $m{s^{ - 1}}$