$A$ block is placed on a parabolic shape ramp given by the equation $y = \frac{x^2}{20}$. If the coefficient of static friction $\mu_s$ is $0.5$,then what is the maximum height above the ground at which the block can be placed without slipping (in $m$)?

The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficient of friction between the body and the inclined plane is $\frac{1}{2 \sqrt{3}}$,then the angle of the inclined plane is (in $^{\circ}$)

$Assertion$: Mountain roads rarely go straight up the slope.
$Reason$: The slope of mountains is large,therefore there are more chances for a vehicle to slip from the roads.

$A$ rough inclined plane is placed on a car moving with a constant velocity $u$ on horizontal ground. $A$ block of mass $M$ rests on the inclined plane. Is any work done by the force of friction between the block and the inclined plane? Is there any dissipation of energy?

$A$ cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of $\frac{g}{2}$. The value of the coefficient of kinetic friction is:

Consider a block kept on an inclined plane (inclined at $45^{\circ}$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down,the coefficient of friction between the block and inclined plane $(\mu)$ is equal to