$A$ car is moving on a horizontal curved road with radius $50\,m$. The approximate maximum speed of the car will be $............\,ms^{-1}$,if the coefficient of friction between the tyres and the road is $0.34$. [Take $g = 10\,ms^{-2}$]

$A$ disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. $A$ coin placed at a distance of $1.25\,cm$ from the axis of rotation remains at rest on the disc. Find the coefficient of friction between the coin and the disc. (Take $g = 10\,m/s^2$)

On which road do we get maximum speed: a circular road with a slope (banked road) or a level circular road?

$A$ bike moving at a speed of $60 \; km/hr$ takes a turn with a radius of $0.1 \; km$. At what angle with the vertical should the bike be tilted to avoid slipping?

$A$ 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

$A$ car has to move on a level turn of radius $450\,m.$ If the coefficient of static friction between the tyre and the road is $\mu = 0.2,$ find the maximum speed the car can take without skidding in $m/s.$