Two masses $A$ and $B$ of $10\,kg$ and $5\,kg$ respectively are connected by a string passing over a frictionless pulley fixed at the corner of a table. The coefficient of friction between mass $A$ and the table is $0.2$. The minimum mass of $C$ that must be placed on $A$ to prevent it from moving is equal to $...........\,kg$.

For the given system,which of the following relations holds between $T_1$,$T_2$,and $T_3$?

$A$ block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m/s$ is $v = N/10$. Then $N$ is:

$A$ car accelerates on a horizontal road due to the forces exerted by

Two blocks of masses in the ratio $m:n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest,then the acceleration of the centre of mass of the system of the blocks is ($g$ = acceleration due to gravity).

$A$ 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.