$A$ vehicle is moving with a velocity $v$ on a curved road of width $b$ and radius of curvature $R$. For counteracting the centrifugal force on the vehicle,the difference in elevation required between the outer and inner edges of the road is

How is centripetal force provided during motion on a level circular path?

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 the coefficient of friction between the cycle tyres and the road is:

An inextensible string of length $\ell$ fixed at one end,carries a mass $m$ at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end,the tension in the string is [The string makes an angle $\theta$ with the vertical]

$A$ child is on a merry-go-round, standing at a distance $2 \ m$ from the centre. The coefficient of static friction between the child and the surface of the merry-go-round is $0.8$. At what maximum angular velocity can the merry-go-round be rotated before the child slips (in $rad/s$)? (Take $g = 10 \ m/s^2$)

$A$ motor car has a width of $1.1 \ m$ between its wheels. Its center of gravity is $0.62 \ m$ above the ground and the coefficient of friction between the wheels and the road is $0.8$. What is the maximum possible speed in $m/s$ if the center of gravity moves in a circle of radius $15 \ m$ on a horizontal road surface?