A block of mass $10\, kg$ is placed on a rough horizontal surface having coefficient of friction $\,\mu  = 0.5$. If a horizontal force of $100\, N$ is acting on it, then acceleration of the block will be ....... $m/s^2$

A uniform wooden stick of mass $1.6 \mathrm{~kg}$ 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 focr. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the st $ck$. The ratio $h / l$ and the frictional force $f$ at the bottom of the stick are $\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$

Given below are two statements:

$Statement$ $(I)$ : The limiting force of static friction depends on the area of contact and independent of materials.

$Statement$ $(II)$ : The limiting force of kinetic friction is independent of the area of contact and depends on materials.

In the light of the above statements, choose the most appropriate answer from the options given below:

A heavy box is solid across a rough floor with an initial speed of $4 \,m / s$. It stops moving after $8$ seconds. If the average resisting force of friction is $10 \,N$, the mass of the box (in $kg$ ) is .....

A body of weight $64\, N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively, the acceleration of the body will be (Acceleration due to gravity $= g$)

$STATEMENT-1$ It is easier to pull a heavy object than to push it on a level ground. and

$STATEMENT-2$ The magnitude of frictional force depends on the nature of the two surfaces in contact.