Centripetal and Centrifugal Forces

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 vehicle of mass $200 \mathrm{kg}$ is moving along a levelled curved road of radius $70 \mathrm{m}$ with angular velocity of $0.2 \mathrm{rad} {\mathrm{s}}^{-1}$. The centripetal force acting on the vehicle is:

A small block of mass $100 \mathrm{g}$ is tied to a spring of spring constant $7.5 \mathrm{N} {\mathrm{m}}^{-1}$ and length $20 \mathrm{cm}.$ The other end of spring is fixed at a particular point $A.$ If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$about point $A,$ then tension in the spring is

A toy car of mass $80 \mathrm{g}$ is maintained to move in a horizontal circle of radius $0.8 \mathrm{m}$ with a velocity $v \mathrm{m} {\mathrm{s}}^{-1}$. If the centripetal force acting on it is $10 \mathrm{N}$, then the value of $v$ in $\mathrm{m} {\mathrm{s}}^{-1}$ is

Centripetal and centrifugal force cancel each other.

How is centripetal force related to centrifugal force?

Define centripetal force with its direction.

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,

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

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?

A particle of charge-q & mass $m$ moves in a circle of radius $r$ around an infinitely long line charge on linear charge density $+\lambda .$ Then time period will be

Name the acceleration experienced by an object in a circular motion, along the radius, towards the centre of the circle.

A ring rotates about $z$-axis as shown in figure. The plane of rotation is $xy$. At a certain instant the acceleration of a particle $P$ (shown in figure)
on the ring is $(6\hat{\mathrm{i}}-8\hat{\mathrm{j}})\mathrm{m}/{\mathrm{s}}^2.$ Find magnitudes of angular acceleration of the ring and its angular velocity at that instant. Radius of the ring is $2 m$ :-

When a point on the rim of a $0.30 \mathrm{m}$ radius wheel experiences a centripetal acceleration of $4.0 \mathrm{m} {\mathrm{s}}^{-2},$what tangential acceleration does that point experience?

A body is projected with a speed $\text{'}u\text{'}$ at an angle ' $\theta$ ' with the honizontal. The radius of curvature of the trajectory when it makes an angle $\left(\frac{\theta }{2}\right)$ with the horizontal is ($g$-acceleration due to gravity)

Two balls of masses $M=9 \mathrm{g}$ and $m=3 \mathrm{g}$ are attached by massless threads $AO$ and $OB$. The length $AB$ is $1 \mathrm{m}$. They are set in rotational motion in a horizontal plane about a vertical axis at $O$ with constant angular velocity $\omega$. The ratio of lengths $AO$ and $OB \left(\frac{AO}{OB}\right)$ for which the tension in threads are same will be,