A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial position with respect to the table, the ball
I. Remains stationary if there is no friction between the paper and the ball.
II. Moves to the left and starts rolling backwards, i.e. to the left if there is a friction between the paper and the ball.
III. Moves forward, i.e., in the direction in which the paper is pulled.
Here, the correct statements is/are

A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, then

A block of mass $5 \mathrm{k}\mathrm{g}$ is (i) pushed in case $\left(\mathrm{A}\right)$ and (ii) pulled in case $\left(\mathrm{B}\right),$ by a force $\mathrm{F}=20\mathrm{ }\mathrm{N},$ making an angle of ${30}^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu =0.2.$ The difference between the accelerations of the block, in case $\left(\mathrm{B}\right)$ and case $\left(\mathrm{A}\right)$ will be:
$\left(\mathrm{g}=10\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}\right)$

Consider the system shown below.

A horizontal force $F$ is applied to a block $X$ of mass $8 \mathrm{kg}$ such that the block $Y$ of mass $2 \mathrm{kg}$ adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block $X$. The coefficient of friction between the surfaces of the blocks $X$ and $Y$ is $0.5$. Take acceleration due to gravity to be $10 \mathrm{m} {\mathrm{s}}^{-2}$. The minimum value of $F$ is