$A$ block kept on a rough surface starts sliding when the inclination of the surface is $\theta$ with respect to the horizontal. The coefficient of static friction between the block and the surface is

$A$ 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:

$A$ car is going at a speed of $6\, m/s$ when it encounters a $15\, m$ slope of angle $30^o$. The friction coefficient between the road and tyre is $0.5$. The driver applies the brakes. The minimum speed of the car with which it can reach the bottom is ........ $m/s$. $(g = 10\, m/s^2)$

$A$ block of mass $2 \, kg$ is placed on a rough inclined plane as shown in the figure $(\mu = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of .............. $cm$.

$Assertion$ : Angle of repose is equal to the angle of limiting friction.
$Reason$ : When the body is just at the point of motion, the force of friction in this stage is called limiting friction.

An inclined plane of length $5.60 \ m$ making an angle of $45^{\circ}$ with the horizontal is placed in a uniform electric field $E = 100 \ V \ m^{-1}$. $A$ particle of mass $1 \ kg$ and charge $10^{-2} \ C$ is allowed to slide down from rest from the maximum height of the slope. If the coefficient of friction is $0.1$,the time taken by the particle to reach the bottom is . . . . . . .