Centripetal and Centrifugal Forces

A chain of mass $M$ and radius $R$ placed on a smooth table is revolving with $v$ about a vertical axis coinciding with the symmetry axis of the chain. Find tension in the chain.

A wire which is bent in the shape of a curve given by, $y=a^3{x}^4.$ A bead of mass m is located at point $P\left(x\mathit{,}y\right)$ If the wire is smooth, find $\omega$ with which wire needs to be rotated for bead to be static.

On the centre of a frictionless table, a small hole is made, through which a weightless string of length $2l$ is inserted. On the two ends of the string, two balls of the same mass $m$ are attached. The arrangement is made in such a way that half of the string is on the table top and half is hanging below. The ball on the table top is made to move in a circular path with a constant speed $v$. What is the centripetal acceleration of the moving ball?

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with constant angular acceleration $\alpha .$ If the coefficient of friction between the rod and the bead is $\mu ,$ and gravity is neglected, then the time after which the bead starts slipping is

A motorcycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

A coin is placed on a rotating turn table rotated with angular speed $\omega .$ The coin just slips if it is placed at $4 \mathrm{cm}$ from the centre of the table. If angular velocity is doubled, at what distance will coin starts to slip?

If the radius of curvature of the path of two particles of same masses are in the ratio $1:2$, then in order to have constant centripetal force, their velocity should be in the ratio of
 

A proton of mass $1.6\times {10}^{-27} \mathrm{kg}$ goes round in a circular orbit of radius $0.10 \mathrm{m}$ under a centripetal force of $4\times {10}^{-13}\mathrm{N}$. The frequency of revolution of the proton is about

A $100 \mathrm{kg}$ car is moving with a maximum velocity of $9 \mathrm{m} {\mathrm{s}}^{-1}$ across a circular track of radius $30 \mathrm{m}.$ The maximum force of friction between the road and the car is

A $500 \mathrm{kg}$ car takes a round turn of radius $50 \mathrm{m}$ with a velocity of $36 \mathrm{km} {\mathrm{hr}}^{-1}$. The centripetal force is

A toy cart is tied to the end of an unstretched string of length $l$, When revolved, the toy cart moves in a horizontal circle with radius $2l$ and time period $T$. If it is speeded until it moves in a horizontal circle of radius $3l$ with period $T_1\text{,}$ $T_1$ is (Hooke's law is obeyed)

A string breaks if its tension exceeds $10 \mathrm{Newton}$. 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 body of mass $m$ performs $\mathrm{U}.\mathrm{C}.\mathrm{M}.$ along a circular path of radius $r$ with a velocity $v$. If its angular momentum is $L$, then its centripetal force is

A cyclist turns around a curve at $15 \mathrm{miles} \mathrm{per} \mathrm{hour}$. If he turns at double the speed, the tendency to overturn is

If tension in a string is $6.4 \mathrm{N}$. A load at the lower end of a string is $0.1 \mathrm{kg}$, the length of the string is $6 \mathrm{m}$ then find its angular velocity $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The magnitude of the centripetal force acting on a body of mass $m$ executing uniform motion in a circle of radius $r$ with speed $v$ is

A particle of mass m is executing uniform circular motion on a path of radius $r$. If $p$ is the magnitude of its linear momentum, the radial force acting on the particle is
 

One end of the string of length $l$ is connected to a particle of mass $m$ and the other end is connected 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) will be ($T$ represents the tension in the string)

Centripetal force in vector form can be expressed as

A car of mass $1000 \mathrm{kg}$ moves on a circular path with constant speed of $12 \mathrm{m} {\mathrm{s}}^{-1}$. It turned through $90°$after travelling $471 \mathrm{m}$ on the road. The centripetal force acting on the car is,