$A$ block of wood resting on an inclined plane of angle $30^o$ just starts moving down. If the coefficient of friction is $0.2$,its velocity (in $ms^{-1}$) after $5\, s$ is: $(g = 10\, ms^{-2})$

Consider a small block sliding down an inclined plane of inclination $30^{\circ}$ with the horizontal. The coefficient of friction is $\mu = \frac{2}{3} x$, where $x$ is the distance (in meters) through which the mass slides down. The distance covered by the mass before it stops is

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on an identical inclined smooth plane. Both inclined planes are at $45^\circ$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and the block is . . . . . . .

$A$ block of mass $8 \ kg$ is at rest on a rough inclined plane as shown in the figure. The magnitude of the net force exerted by the surface on the block will be $..... \ N$. (Take $g = 10 \ m/s^2$)

$A$ block of mass $10 \,kg$ is held at rest against a rough vertical wall $[\mu=0.5]$ under the action of a force $F$ as shown in the figure. The minimum value of $F$ required for it is ............ $N$ $(g=10 \,m/s^2)$.

$A$ solid hemisphere of weight $P$ rests with its curved surface in contact with a rough inclined plane. $A$ weight $Q$ is placed at some point on the rim of the hemisphere to keep its plane surface horizontal. Then its minimum coefficient of friction is