$A$ block of mass $m$ is lying on an inclined plane. The coefficient of friction between the plane and the block is $\mu$. The force $(F_1)$ required to move the block up the inclined plane will be

$A$ particle is placed at rest inside a hollow hemisphere of radius $R$. The coefficient of friction between the particle and the hemisphere is $\mu = \frac{1}{\sqrt{3}}$. The maximum height up to which the particle can remain stationary is

Two touching blocks $1$ and $2$ are placed on an inclined plane forming an angle $60^{\circ}$ with the horizontal. The masses are $m_1$ and $m_2$ and the coefficients of friction between the inclined plane and the two blocks are $1.5 \mu$ and $1.0 \mu$, respectively. The force of reaction between the blocks during the motion is ($g=$ acceleration due to gravity).

$A$ 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).

$A$ 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 $1 \ kg$ is pushed up a surface inclined to the horizontal at an angle of $60^{\circ}$ by a force of $10 \ N$ parallel to the inclined surface as shown in the figure. When the block is pushed up by $10 \ m$ along the inclined surface,the work done against the frictional force is: $\left[g=10 \ m/s^2, \mu_s = 0.1\right]$