$A$ block of mass $m$ is at rest on an inclined plane with an angle of inclination $\theta$ and coefficient of friction $\mu$,as shown in the figure. The frictional force acting on the block is:

The time taken by an object to slide down a $45^{\circ}$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is:

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is $60^{\circ}$ is

$A$ block of mass $10\, kg$ is placed on an inclined plane. When the angle of inclination is $30^\circ$,the block just begins to slide down the plane. The force of static friction is ....... $kg\, wt$.

$A$ block of mass $m_1=1 \ kg$ and another mass $m_2=2 \ kg$ are placed together (see figure) on an inclined plane with an angle of inclination $\theta$. Various values of $\theta$ are given in List $I$. The coefficient of friction between the block $m_1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_2$ and the plane are equal to $\mu=0.3$. In List $II$,expressions for the friction on block $m_2$ are given. Match the correct expression of the friction in List $II$ with the angles given in List $I$,and choose the correct option. The acceleration due to gravity is denoted by $g$. [Useful information: $\tan(5.5^{\circ}) \approx 0.1; \tan(11.5^{\circ}) \approx 0.2; \tan(16.5^{\circ}) \approx 0.3$]

List $I$	List $II$
$P. \theta=5^{\circ}$	$1. m_2 g \sin \theta$
$Q. \theta=10^{\circ}$	$2. (m_1+m_2) g \sin \theta$
$R. \theta=15^{\circ}$	$3. \mu m_2 g \cos \theta$
$S. \theta=20^{\circ}$	$4. \mu(m_1+m_2) g \cos \theta$

$A$ block of mass $5 \ kg$ is kept against an accelerating wedge with a wedge angle of $45^{\circ}$ to the horizontal. The coefficient of friction between the block and the wedge is $\mu = 0.4$. What is the minimum absolute value of the acceleration of the wedge to keep the block steady? Assume $g = 10 \ m \ s^{-2}$.