$A$ box is placed on an inclined plane and has to be pushed down. The angle of inclination is

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom,if the coefficient of friction for the lower half is given by-

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with a coefficient of friction $\mu$,and the mass $m$ is hanging vertically. The pulley is frictionless. Choose the correct statement$(s)$.

Consider three masses $m_1, m_2$ and $m_3$ $(m_1 > m_2 > m_3)$ that are at rest on an inclined plane as shown in the figure. The angle of inclination $(\theta)$ of the plane is gradually increased until the masses just begin to slide. (Assume the coefficient of static friction between the masses and the surface is constant). Then,which of the following statements is correct?

$A$ block moves down a smooth inclined plane of inclination $\theta$. Its velocity on reaching the bottom is $v$. If it slides down a rough inclined plane of the same inclination,its velocity on reaching the bottom is $v/n$,where $n$ is a number greater than one. The coefficient of friction $\mu$ is given by:

$A$ block slides down an inclined plane with an acceleration $g/2$ as shown in the figure. Then the coefficient of kinetic friction is