Circular Motion and 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.
What should be the minimum angular speed of the turn table so that the masses will slip from this position?

A long playing record revolves with a speed of $33\frac{1}{4}$ rev/min. and has a radius of $15 \mathrm{cm}$.  Two coins are placed at $4 \mathrm{cm}$ and  $14 \mathrm{cm}$ away from the centre of the record. If the coefficients of friction between the coin and the record is $0.15$, which of the two coins will revolve with record ?

A body of mass $0.5 \mathrm{kg}$ is whirled with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ using $0.5 \mathrm{m}$ length string which can withstand a tension of $15 \mathrm{N}$.  Neglecting the force of gravity on the body predict whether the string will break or not.

Which region of the earth experiences maximum centripetal force ?

What provides the centripetal force to a car taking a turn on a level road ?

"A cyclist taking a turn bends inwards, while a passenger in a car taking the same turn is thrown outwards." Why?

What is meant by the banking of roads? What is its purpose?

On what values does the angle of banking depend ?

What is meant by banking of road ? Why should we do that ?

A cyclist wants to loop the loop inside the death globe of diameter $5m$. Find the minimum velocity, that he should have at the lowest point and calculate the height from which he should start it .

What is the maximum speed with which a cyclist can move without skidding in a circular path of radius $10 m$. on a road where the coefficient of friction between tyre and the road is $0.5$

A motorcyclist goes around a circular race curve at $162 km{h}^{-1}$ .To keep his balance he leans inwards ${40}^{\circ }$ from the vertical. What is the radius of the circular path?

A cyclist goes around a circular track of $410 m$ in $20 s$.Find the angle that his cycle makes with vertical.

A cyclist move at a speed of $4.9 m{s}^{-1}$ describes a circle of radius $10 m$.What is the smallest value of the coefficient of friction between the tyres and the ground so that cyclist may be hald in balance.

At what angle must a railway track with a bend of $250 m$ be banked for the safe running of the train at a speed of $72 km{h}^{-1}$

A railway track has its center of gravity at a height of $1.2 m$ above the ground and the rails are $1.5 m$ apart .Calculate the maximum safe speed with which it could travel around an unbanked curve of radius $32 m$.

What is the work done by the centripetal force?

A circular track of radius $300\mathrm{m}$ is banked at an angle of ${15}^{\mathrm{o}}$, if the co-efficient of friction between the wheels of a race car and road is $0.2$. What is the optimum speed of the race car to avoid wear and tear on its types?

What is meant by banking of roads? Obtain an expression for the maximum speed with which a vehicle can safely negotiate a curved road banked at an angle θ, considering the friction is negligible.