$A$ particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{P}$ at any time $t$ is $P_x = 2\cos t$ and $P_y = 2\sin t$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be $\theta = $ ........... $^o$.

$A$ book is lying on the table. What is the angle between the action of the book on the table and the reaction of the table on the book?

Why are porcelain objects wrapped in paper or straw before packing for transportation?

$A$ batsman hits a ball of mass $0.2 \ kg$ straight towards the bowler without changing its initial speed of $6 \ m/s$. What is the impulse imparted to the ball (in $Ns$)?

Three different projectiles,each with the same mass $m$,are fired with speed $v$ at a wall. In case $A$,the projectile bounces straight back with speed $v$. In case $B$,the projectile sticks to the wall. In case $C$,the projectile crashes through the wall and emerges with half its original speed. These three cases are shown in the figure. Place the magnitude of the impulse exerted by the wall on the projectile in each of these three cases in the correct order.

$A$ 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 $0 \leq t \leq T$. The velocity of the particle at the end of the interval is: