$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively:

$A$ cylinder is placed on a rough plank,which in turn is placed on a smooth surface. The plank is pulled with a constant force $F$. Indicate the correct direction of the friction force acting on the cylinder.

When a bicycle is in motion,the force of friction exerted by the ground on the two wheels is such that it acts

$STATEMENT-1$: It is easier to pull a heavy object than to push it on a level ground.
$STATEMENT-2$: The magnitude of frictional force depends on the nature of the two surfaces in contact.

$A$ block of mass $m$ is placed on a smooth horizontal surface. $A$ force making an angle $\theta$ with the horizontal starts acting on the block. The magnitude of the force is constant but its direction with the horizontal changes as $\theta = a + bs$,where $a$ and $b$ are constants and $s$ is the distance covered by the block. If $|F| = 2mb$,find the velocity of the block as a function of the angle $\theta$.

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x_0$ such that $\frac{\mu mg}{K} < x_0 < \frac{2\mu mg}{K}$,and then released. Which of the following statements is correct?