$A$ cylinder is placed on a rough plank,which in turn is placed on a smooth surface. The plank is pulled with a constant force $F$. Indicate the correct direction of the friction force acting on the cylinder.

$A$ block of mass $M = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $\mu = 0.05.$ When hit by a bullet of mass $m = 50\,g$ moving with speed $v,$ which gets embedded in it,the block moves and comes to a stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,m/s^2,$ the value of $H$ is close to ................. $km$.

Two blocks $A$ and $B$ of masses $5 \ kg$ and $10 \ kg$ respectively are placed as shown in the figure. The coefficient of friction between all the surfaces is $0.2$. $A$ force $F$ is applied on block $A$ at an angle of $30^{\circ}$ with the horizontal. If the system moves with constant acceleration,find the acceleration of block $B$. (Assume $g = 10 \ m/s^2$ and $F = 100 \ N$) (in $m/s^2$)

The driver of a car travelling at velocity $v$ suddenly sees a broad wall in front of him at a distance $d$. He should

Two masses $m_1 = 5 \ kg$ and $m_2 = 10 \ kg$,connected by an inextensible string over a frictionless pulley,are arranged as shown in the figure. The coefficient of friction of the horizontal surface is $0.15$. The minimum mass $m$ that should be placed on top of $m_2$ to stop the motion is ........ $kg$. (in $.3$)

$A$ 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?