$A$ person with a machine gun can fire $50 \ g$ bullets with a velocity of $240 \ m/s$. $A$ $60 \ kg$ tiger moves towards him with a velocity of $12 \ m/s$. In order to stop the tiger in its track,the number of bullets the person must fire towards the tiger is:

$A$ bullet of mass $0.1\, kg$ is fired into a wooden block to pierce through it,but it stops after moving a distance of $50\, cm$ into it. If the velocity of the bullet before hitting the wood is $10\, m/s$ and it slows down with uniform deceleration,then the magnitude of the effective retarding force on the bullet is $'x'\, N$. The value of $'x'$ to the nearest integer is:

Calculate the acceleration (in $m/s^{2}$) of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is $0.05$. (Given: $g = 10\; m/s^{2}$,mass of the string is negligible and no other friction exists).

$A$ $10 \,g$ bullet moving at $200 \,m/s$ stops after penetrating $5 \,cm$ of a wooden plank. The average force exerted on the bullet will be .......... $N$.

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

Three forces of magnitude $F_1, F_2$ and $F_3$ act on a body located at the origin as shown in the figure. The condition that gives zero net force is