Dynamics of 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?

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 coin placed on a rotating turntable just slips if it is placed at a distance of $4 \mathrm{cm}$ from the center. If the angular velocity of the turntable is doubled, it will just slip at a distance of 

A car moves at a constant speed on a road as shown in the figure. If the normal force applied by the road on the car, $N_{\mathrm{A}}$ and $N_{\mathrm{B}}$, when it is at the points $A$ and $B$, respectively, then?

A small bead of mass $m$ is carried by a circular hoop having centre at $\mathrm{O}$ and radius $=\sqrt{2}\mathrm{ }\mathrm{m}$ which rotates about a fixed vertical axis. The coefficient of friction between bead and hoop is $\mathrm{\mu }=0.5$. The maximum angular speed of the hoop for which the bead does not have relative motion with respect to the hoop is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ .

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$, the net force on the particle (directed towards the centre) is: (Where $T$ is the tension in the string) [Choose the correct alternative].

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 weightless thread can bear tension upto $3.7\mathrm{ }\mathrm{kg}.$ A stone of mass $500 \mathrm{g}$ is tied to it and revolved in a circular path of radius $4 \mathrm{m}$ in a vertical plane. If $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the maximum angular velocity of the stone will be

An object of mass 0.4 kg is whirled in a horizontal circle of radius 2m. If it performs 60 revolutions min^-1, calculate the centripetal force acting on it.

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

A circular curve of a highway is designed for traffic moving at $72 \mathrm{km} {\mathrm{h}}^{-1}$. If the radius of the curved path is $100 \mathrm{m}$, the correct angle of banking of the road should be given by

A car is moving in a circular horizontal track of radius $10 \mathrm{m}$ with a constant speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. And a rod is hanging in the car.  The angle made by the rod with track is

A centripetal force acts

Choose the correct statement from the following