$A$ car is driven on a banked road of radius of curvature $20 \ m$ with maximum safe speed. In order to increase its safe speed by $10 \%$,the increase in the radius of curvature will be (Angle of banking and friction is unchanged in both the cases.) (in $m$)

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

$A$ body of mass $M \text{ kg}$ is at the top point of a smooth hemisphere of radius $5 \text{ m}$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \text{ m/s}$. At this instant, the angle made by the radius vector of the body with the vertical is (Acceleration due to gravity $g = 10 \text{ m/s}^2$) (in $^{\circ}$)

$A$ motor vehicle of mass $1000 \,kg$ is moving on a circular road having a banking angle of $30^{\circ}$ and a coefficient of friction of $0.2$. Then the normal reaction force on the motor vehicle is about (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,N$)

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 $0.2$.

$A$ coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$,the maximum angular velocity which can be given to the disc,so that the coin does not slip away,is: