$A$ block of mass $15\,kg$ is resting on a rough inclined plane as shown in the figure. The block is tied up by a horizontal string which has a tension of $50\,N$. The coefficient of friction between the surface of contact is: $(g = 10\,m/s^2)$

$A$ block of mass $m$ is placed on a wedge of angle $\theta$. The wedge is moving with a constant velocity $v$ on a horizontal surface. If the block does not slide on the wedge,find the work done by the friction force on the block in time $t$.

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............$cm$.

$A$ particle is projected up along a rough inclined plane of inclination $45^{\circ}$ with the horizontal. If the coefficient of friction is $0.5$,the acceleration is ($g=$ Acceleration due to gravity).

$A$ 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 ..... .

$A$ body is placed on a rough inclined plane of inclination $\theta$. As the angle $\theta$ is increased from $0^o$ to $90^o$,the contact force between the block and the plane