The force required just to move a body up an inclined plane is double the force required just to prevent the body from sliding down. If $\mu$ is the coefficient of friction,the inclination of the plane to the horizontal is:

$A$ $2 \ kg$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to the horizontal axis. The coefficient of static friction between their surfaces is:

$A$ car of weight $W$ is on an inclined road that rises by $100 \, m$ over a distance of $1 \, km$ and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 \, m/s$,the car needs power $P$. If it needs power $\frac{P}{2}$ while moving downhill at speed $v$,then the value of $v$ is ........ $m/s$.

$A$ block of mass $10 \,kg$ is held at rest against a rough vertical wall $[\mu=0.5]$ under the action of a force $F$ as shown in the figure. The minimum value of $F$ required for it is ............ $N$ $(g=10 \,m/s^2)$.

$A$ bob of mass $m$ is attached to a string of length $\ell$ whose other end is tied to a light vertical rod as shown in the figure. The bob is swinging in a horizontal plane with a constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is the minimum friction coefficient between the ground and the block for which the block does not slip?

Two blocks $A$ and $B$ of equal masses are sliding down along straight parallel lines on an inclined plane of $45^{\circ}$. Their coefficients of kinetic friction are $\mu_A = 0.2$ and $\mu_B = 0.3$ respectively. At $t = 0$,both the blocks are at rest and block $A$ is $\sqrt{2} \text{ m}$ behind block $B$. Calculate the time and distance from the initial position where the front faces of the blocks come in line on the inclined plane as shown in the figure. (Use $g = 10 \text{ m/s}^2$)