FOR DIFFERENT COMPETITIVE EXAMINATIONS

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, then the maximum possible value of $\alpha$ is given by :

A block of mass  $m$ is placed on a surface with a vertical cross-section given by $y=\frac{x^3}{6}$. If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is:

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

A $2 \mathrm{kg}$ block is placed on a rough surface inclined at  $30°$ with the horizontal. If the coefficient of friction be $0.5$, the limiting frictional force acting on the block will be:

Lubricants cannot reduce:

Polishing the surfaces in contact beyond a limit increases friction because:

A block of base $10 \mathrm{cm}\times 10 \mathrm{cm}$ and height $15 \mathrm{cm}$ is kept on an inclined plane. The coefficient of friction between them is $\sqrt{3}$. The inclination $\mathrm{\theta }$ of this inclined plane from the horizontal plane is gradually increased from $0°$. Then 

A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is  $\mu$ and  $\tan \theta >\mu$. The block is held stationary by applying a force $F$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $F$is varied from$F_1=mg \left(\sin \theta -\mu \cos \theta \right) to F_2=mg \left(\sin \theta +\mu \cos \theta \right)$ the frictional force $f$ versus $F$ graph will look like: