$A$ ball connected with a string is released at an angle of $45^{\circ}$ with the vertical,as shown in the figure. If the mass of the box is equal to the mass of the ball,the acceleration of the box at this instant will be:

$A$ helicopter of mass $1000 \;kg$ rises with a vertical acceleration of $15\; m s^{-2}$. The crew and the passengers weigh $300\; kg$. Give the magnitude and direction of the
$(a)$ force on the floor by the crew and passengers,
$(b)$ action of the rotor of the helicopter on the surrounding air,
$(c)$ force on the helicopter due to the surrounding air.

$A$ block of mass $5 \text{ kg}$ is in contact with a vertical wall as shown. Find the friction force acting on the block. (in $\text{ N}$)

Four blocks $A, B, C$ and $D$ of masses $6 \,kg, 3 \,kg, 6 \,kg$ and $1 \,kg$ respectively are connected by light strings passing over frictionless pulleys as shown in the figure. The strings $P$ and $Q$ are horizontal. The coefficient of friction between the horizontal surface and the block $B$ is $0.2$ and the blocks $A$ and $B$ move together. If the system is released from rest, then the tension in the string $Q$ is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,N$)

$A$ 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:

When milk is churned,cream gets separated due to