In the figure,a ball of mass $m$ is tied with two strings of equal length as shown. If the rod is rotated with angular velocity $\omega$,then

$A$ horizontal force $12 \, N$ pushes a block weighing $1/2 \, kg$ against a vertical wall. The coefficient of static friction between the wall and the block is $0.5$ and the coefficient of kinetic friction is $0.35$. Assuming that the block is not moving initially,which one of the following choices is correct? (Take $g = 10 \, m/s^2$)

$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts equal and opposite forces for the same time $t$ on each toy cart. If the coefficients of friction $\mu$ between the ground and the toy carts are equal,then the ratio of the displacements of the toy carts is:

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(1)$ remains stationary if there is no friction between the paper and the ball.
$(2)$ moves to the left and starts rolling backwards,i.e.,to the left,if there is friction between the paper and the ball.
$(3)$ moves forward,i.e.,in the direction in which the paper is pulled.
Here,the correct statement$(s)$ is/are:

Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
$(B)$ When a body is at rest,it must be in equilibrium.

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$