$A$ 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 $m$)?

$A$ small mass slides down an inclined plane of angle $\theta$ with the horizontal. The coefficient of friction is $\mu = \mu_0 x$,where $x$ is the distance through which the mass slides down and $\mu_0$ is a constant. Then,the distance covered by the mass before it stops is:

As shown in the figure,a body of mass $m$ moving vertically downward with a speed of $3\, m/s$ hits a smooth fixed inclined plane and rebounds with a velocity $v_f$ in the horizontal direction. If the angle of the inclined plane is $30^{\circ}$,the velocity $v_f$ will be:

$A$ body of mass $m$ is launched up on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$. If the time of ascent is half of the time of descent,the value of $x$ is ..... .

$A$ box is lying on an inclined plane. What is the coefficient of static friction if the box starts sliding when the angle of inclination is $60^\circ$?

$A$ force of $750 \, N$ is applied to a block of mass $102 \, kg$ to prevent it from sliding on a plane with an inclination angle $30^{\circ}$ with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are $0.4$ and $0.3$ respectively,then the frictional force acting on the block is...... $N$.