Two cars of masses $m_1$ and $m_2$,joined back to back by a massless compressed spring,are at rest on a horizontal rough road. When the compression of the spring is suddenly removed,the cars move away from each other and come to rest due to friction. If the frictional force is the same on both cars,what is the ratio of their stopping times?

One end of a spring of force constant $150 \text{ dyne cm}^{-1}$ is connected to a block of mass $0.2 \text{ kg}$ kept on a rough horizontal surface of coefficient of friction $0.3$. The other end of the spring is connected to a rigid support as shown in the figure and the spring is initially undeformed. The maximum velocity $v$ that can be given to the block so that it travels only in one direction is . . . . . . $\text{ms}^{-1}$. (Acceleration due to gravity $= 10 \text{ ms}^{-2}$)

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

For the given system,find the value of $\theta_2$.

$A$ person used force $(F)$,shown in the figure,to move a load with a constant velocity on a given surface. Identify the correct surface profile.

$A$ constant force $F$ is applied in the horizontal direction as shown. If the contact force between $M$ and $m$ is $N$ and the contact force between $m$ and $M'$ is $N'$,then: