With what minimum velocity should block be projected from left end $A$ towards end $B$ such that it reaches the other end $B$ of conveyer belt moving with constant velocity $v$. Friction coefficient between block and belt is $\mu$ .
$\sqrt {\mu gL} $
$\sqrt {2\mu gL} $
$\sqrt {3\mu gL} $
$2\sqrt {\mu gL} $
A circular racetrack of radius $300\; m$ is banked at an angle of $15^o$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$, what is the
$(a)$ optimum speed of the racecar to avoid wear and tear on its tyres, and
$(b)$ maximum permissible speed to avoid slipping ?
$Assertion$ : Angle of repose is equal to the angle of limiting friction.
$Reason$ : When the body is just at the point of motion, the force of friction in this stage is called limiting friction.
A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, then
......... $m/s^2$ is magnitude of acceleration of a block moving with speed $10\,m/s$ on a rough surface if coefficient of friction is $0.2$.
Two blocks $A$ and $B$ are released from the top of a rough inclined plane so that $A$ slides along the plane and $B$ falls down freely. Which will have higher velocity on reaching the ground ?