$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is (in $^{\circ}$)

$A$ block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{v_{0}}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$. The nearest integer to $I$ is......

$A$ block of weight $1 \,N$ rests on an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu$. The minimum force that has to be applied parallel to the inclined plane to make the body just move up the plane is

An inclined plane is bent in such a way that the vertical cross-section is given by $y = \frac{x^2}{4}$,where $y$ is in the vertical direction and $x$ is in the horizontal direction. If the upper surface of this curved plane is rough with a coefficient of friction $\mu = 0.5$,the maximum height in $cm$ at which a stationary block will not slip downward is............$cm$.

The coefficient of friction between two surfaces is $\mu = 0.8$. The tension in the string shown in the figure is ........ $N$.

$A$ heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is $0.25$,then the maximum fraction of length of the chain that can hang over one edge of the table is ...... $\%$