If a cyclist moving with a speed of $4.9\, m/s$ on a level road can take a sharp circular turn of radius $4 \,m$, then coefficient of friction between the cycle tyres and road is

A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu  .$ The coin will revolve with the record if

A racing car travels on a track (without banking) $ABCDEPA$. $ABC$ is a circular arc of radius $2R$. $CD$ and $FA$ are straight paths of length $R$ and $DEF$ is a circular arc of radius $R = 100 \,m$. The coefficient of friction on the road is $\mu = 0.1$. The maximum speed of the car is $50\,ms^{-1}$. Find the minimum time for completing one round.

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

A $70 \;kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\; m$ rotating about its vertical axis with $200\; rev/min$. The coefficient of friction between the wall and his clothing is $0.15 .$ What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

A cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed, the tendency to overturn is