In the figure,a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip,then

$A$ sphere of mass $m$ and radius $R$ is kept on a rough horizontal surface and pulled with a horizontal force $F = \alpha t$,where $\alpha$ is a constant and $t$ is time. The coefficient of static friction is $\mu_s$ and the coefficient of kinetic friction is $\mu_k$. Which of the following graphs correctly shows the variation of the acceleration of the sphere with time?

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring some elongation and then released.

Which is a suitable method to decrease friction?

$A$ 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:
$(A)$ Remains stationary if there is no friction between the paper and the ball.
$(B)$ Moves to the left and starts rolling backwards,$i.e.$,to the left if there is friction between the paper and the ball.
$(C)$ Moves forward,$i.e.$,in the direction in which the paper is pulled.
Which of the following statements is/are correct?

Consider two blocks of mass $m_1 = 5 \, kg$ and $m_2 = 10 \, kg$ placed on a horizontal surface. The coefficient of static friction between the blocks and the surface is $\mu = 0.2$. $A$ horizontal force $F$ is applied to the $10 \, kg$ block. What is the maximum force $F$ (in $N$) that can be applied such that neither block moves? (Take $g = 10 \, m/s^2$)