$A$ uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is $0.5$. If the cylinder is $4\, cm$ in diameter and $10\, cm$ in height,which of the following is the minimum acceleration of the cart needed to cause the cylinder to tip over? (Assume $g = 10\, m/s^2$)

$A$ force of $mg$ is applied to block $B$ to keep the system in equilibrium. Find the value of $T_1$.

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 $\,N$)

From Newton's second law of motion,it can be inferred that

$Assertion$: Two bodies of masses $M$ and $m$ $(M > m)$ are allowed to fall from the same height. If the air resistance for each is the same,then both bodies will reach the Earth simultaneously.
$Reason$: For the same air resistance,the acceleration of both bodies will be the same.

In the following problem,indicate the correct direction of the friction force acting on the cylinder,which is pulled on a rough surface by a constant force $F$. $A$ spool is pulled horizontally by a constant force $F$ applied below the center of mass. Which of the following diagrams correctly shows the direction of the friction force?