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

$A$ packet of weight $W$ dropped from a parachute strikes the ground and comes to rest with retardation equal to twice the acceleration due to gravity. The force exerted on the ground is

$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

Place a uniform meter scale horizontally on your extended index fingers with the left one at $0.00 \ cm$ and the right one at $90.00 \ cm$. When you attempt to move both fingers slowly towards the center,initially only the left finger slips with respect to the scale and the right finger does not. After some distance,the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_R$ from the center $(50.00 \ cm)$ of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are $0.40$ and $0.32$,respectively,the value of $x_R$ (in $cm$) is:

$A$ boy of mass $4 \, kg$ is standing on a piece of wood having mass $5 \, kg$. If the coefficient of friction between the wood and the floor is $0.5$,the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ...... $N$. (Round off to the Nearest Integer) [Take $g = 10 \, m s^{-2}$]

$A$ $500 \, kg$ horse pulls a cart of mass $1500 \, kg$ along a level road with an acceleration of $1 \, m/s^2$. If the coefficient of sliding friction is $0.2$,then the force exerted by the horse in the forward direction is ......... $N$.