A block of mass $10\; \mathrm{kg}$ is in contact against the inner wall of a hollow cylindow cylindrical drum of radius $1 \;\mathrm{m}$. The coeffident of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ......$rad/s$ $\left(g-10 m / s^{2}\right)$

A car is moving on a circular path and takes a turn. If ${R_1}$ and ${R_2}$ be the reactions on the inner and outer wheels respectively, then

A motorcyclist of mass m is to negotiate a curve of radius r with a speed v. The minimum value of the coefficient of friction so that this negotiation may take place safely, is

One end of string of length $l$ is connected to a particle of mass $'m'$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed $'v',$ the net force on the particle (directed towards centre) will be ($T$ represents the tension in the string) 

A coin placed on a rotating table just slips if it is placed at a distance $4r$ from the centre. On doubling the angular velocity of the table, the coin will just slip when at a distance from the centre equal to

Find the maximum velocity for skidding for a car moved on a circular track of radius $100\, m$. The coefficient of friction between the road and tyre is $0.2$ ....... $m/s$