Banking of Roads

Two blocks of mass $m_1=10 \mathrm{kg}$ and $m_2=5 \mathrm{kg},$ connected to each other by a massless inextensible string of length $0.3 \mathrm{m}$ are placed along a diameter of a turn table. The coefficient of friction between the table and $m_1$ is $0.5$ while there is no friction between $m_2$ and the table. The table is rotating with an angular velocity of $10$ rad $s^{-1}$ about a vertical axis passing through its centre $O$. The masses are placed along the diameter of the table on either side of the centre $O$ such that the mass $m_1$ is at a distance of $0.124 \mathrm{m}$ from $O$. The masses are observed to be at rest with respect to an observer on the turn table. Calculate the frictional force on $m_1$.

Three particles, each of mass $m,$ are situated at the vertices of an equilateral triangle of side length $a$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original mutual separation $a$. Find the initial velocity that should be given to each particle and also the time period of the circular motion.

A car travels on a banked horizontal road with inclination $45°$. What is its maximum speed for not skidding up $\left(\mu =0.75,R=200\right)$.

A car is moving on a circular road of radius $150 \mathrm{m}$ with a coefficient of friction $0.6$. With what optimum velocity should the car be moved so that it crosses the turn safely.:

A body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then,

A particle starts circular motion with radius $\mathrm{R}$ about a fixed point with uniform angular acceleration $2 \mathrm{rad}/{\sec }^2$. If the time at which net
force on particle makes an angle $45°$ with direction of its velocity is $\frac{1}{\sqrt{\mathrm{n}}}\sec .$ Then value of $\mathrm{n}$ is :-

A string breaks if its tension exceeds $10 \mathrm{N}$. A stone of mass $250 \mathrm{g}$, tied to this string of length $10 \mathrm{cm}$, is rotated in a horizontal circle. The maximum angular velocity of rotation can be,

A car of mass $2000 \mathrm{Kg}$ is moving with a speed of 10 $\mathrm{m}{\mathrm{s}}^{-1}$on a circular path of radius $20 \mathrm{m}$ on a level road. What must be the frictional force between the car and the road so that the car does not slip?

The minimum velocity (in $\mathrm{m}{\mathrm{s}}^{-1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

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

If a car moves on a circular banked road the centripetal force may be provided by :-

A biker initially at rest, starts to move on a circular path of radius $R=\frac{200}{7} \mathrm{km}$  with tangential acceleration $a = 1 \mathrm{m} {\sec }^{-2}$ (constant in magnitude). If on an average bike runs $50 \mathrm{km} {\mathrm{litre}}^{-1}$ and initially the bike has $2 \mathrm{litre}$ petrol. The minimum value of the coefficient of friction, so, that bike will not slip during motion is 

A stone of mass $0.03 \mathrm{kg}$ attached to a $1.5 \mathrm{m}$ long string is whirled around in a horizontal circle at a speed of $6 {\mathrm{ms}}^{-1}$. The tension in the string is:

When a car of mass $M$ passes through a convex bridge of radius $r$ with velocity $v$, then it exerts a force on it. What is the magnitude of the force?

Which force is an example of a real force?

(Centripetal/ Centrifugal/ Coriolis)

A motor cyclist moving with a velocity of $72 \mathrm{km} {\mathrm{hour}}^{-1}$ on a flat road takes a turn on the road at a point where the radius of curvature of the road is $20 \mathrm{m}$. The acceleration due to gravity is $10 \mathrm{m} {\sec }^{-2}$. In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than