Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction $\mu$. $A$ force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards the right.

$A$ helicopter of mass $2000 \,kg$ rises with a vertical acceleration of $15 \,m s^{-2}$. The total mass of the crew and passengers is $500 \,kg$. Calculate the magnitude and direction of the following (take $g = 10 \,m s^{-2}$):
$(a)$ Force on the floor of the helicopter 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.

$A$ mass of $1 \text{ kg}$ is kept on an inclined plane with $30^\circ$ inclination with respect to the horizontal plane and it is at rest initially. Then, the whole assembly is moved up with a constant velocity of $4 \text{ m/s}$. The work done by the frictional force in time $2 \text{ s}$ is . . . . . . $\text{J}$. (Take $g = 10 \text{ m/s}^2$)

$A$ force of $36 \, \text{dyne}$ acts on a body placed on an inclined plane making an angle of $60^{\circ}$ with the horizontal. If the mass of the body is $18 \, \text{g}$,what is the acceleration of the body in the horizontal direction?

$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. $A$ resistive force of $750 \ N$ acts on it. If the engine produces a power of $30 \ kW$,what is the acceleration of the car in $m/s^2$?

$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by: