A small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has coefficient of friction $\mu $. The ball comes to stop at $C$ after travelling a distance $L$ which is
$\frac{{2h}}{\mu } + \frac{{v_0^2}}{{2\mu g}}$
$\frac{h}{\mu } + \frac{{v_0^2}}{{2\mu g}}$
$\frac{h}{{2\mu }} + \frac{{v_0^2}}{{\mu g}}$
$\frac{h}{{2\mu }} + \frac{{v_0^2}}{{2\mu g}}$
A bag is gently dropped on a conveyor belt moving at a speed of $2\,m / s$. The coefficient of friction between the conveyor belt and bag is $0.4$ Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is $.....m$ [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 a force $F$ as shown in figure. The minimum value of $F$ required for it is ............ $N$ $\left(g=10 \,m / s ^2\right)$
A horizontal force of $4\,N$ is needed to keep a block of mass $0.5\, kg$ sliding on a horizontal surface with a constant speed. The coefficient of sliding friction must be :- $[g = 10\, m/s^2]$
An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by