$A$ metal block is resting on a rough wooden surface. $A$ horizontal force applied to the block is increased uniformly with time,i.e.,$F = kt$. Which of the following curves correctly represents the velocity $v$ of the block as a function of time $t$?

$A$ 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.

If the overbridge is concave instead of being convex,the thrust on the road at the lowest position will be

In the figure,a block of weight $60 \ N$ is placed on a rough surface. The coefficient of friction between the block and the surface is $0.5$. What should be the maximum weight $W$ (in $N$) such that the block does not slip on the surface?

In the figure,a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip,then

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).