Circular Motion

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 particle is moving uniformly on a horizontal circular path. Work done by centripetal force on the particle in one half revolution is

A weightless thread can withstand tension upto $30 \mathrm{N}$. A stone of mass $0.5 \mathrm{kg}$ is tied to it and is revolved in a circular path of radius $2 \mathrm{m}$ in a vertical plane .If $g=10 \mathrm{m}/{\mathrm{s}}^2$, the maximum angular velocity of the stone can be?

A cyclist is moving on a circular path with constant speed $v$. What is the change in its velocity after it has described an angle of $30°$.

A particle of mass $2 \mathrm{kg}$ suspended with the help of sa tring of length $0.72 \mathrm{m}$ is given velocity of $v_0=6 \mathrm{m} {\mathrm{s}}^{-1}$ at its lowest position. Tension in the string at its lowest position is $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A car is moving in a circular horizontal track of radius $10 \mathrm{m}$ with a constant speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. A bob is suspended from the roof of the car by a light wire of length $1.0 \mathrm{m}$. The angle made by the wire with the vertical is (in radian)

If the banking angle of a curved road is ${\tan }^{-1}\left[\frac{3}{5}\right]$ and radius of the curvature of road is $6 \mathrm{m}$. Then the speed for vehicles on the curved road will be:

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 $32 m$.

A plane of mass $M$ is looping in vertical curve path with constant speed of $v$. A man of mass "$m$" is sitting in the plane. At a certain instant $t$, when plane passes through a point $P$ of the curved path, the radius of curvature of curved path is $R$ and normal force "$N$" acting on the man exerted by seat of plane is making angle $\theta$ with vertical. [mass of man is $60\mathrm{kg}$ and $v=\frac{375}{2\sqrt{5}} {\mathrm{ms}}^{-1},R=1250\left(2+\cos \theta \right)$ metre].
Now choose the CORRECT option.