Centripetal Acceleration & Force

The real force F acting on particle of mass m performing circular motion acts along the radius of circle r and is directed forwards the centre of the circle. The magnitude of square root of such a force is (T = periodic time)

Two stones of masses $m$ and $3m$ are whirled in horizontal circles, the heavier one in a radius $\frac{r}{3}$ and the lighter one in radius $r$. When both the stones experience same centripetal forces, the tangential speed of lighter stone is '$n$' times that of the value of heavier stone. The value of '$n$' is

Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is

For a particle moving in a circle with constant angular speed, which of the following statements is 'false'?

Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius $\left(\frac{r}{3}\right)$ and lighter one in a radius r. The tangential speed of lighter stone is ' $n$ ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of $n$ is

The figure shows two masses ' $m$ ' and ' $M$ ' connected by a light string that passes through $\text{a}$ small hole ' $O$ ' at the centre of the table. Mass ' $m$ ' is moved round in a horizontal circle with ' $O$ ' as the centre. The frequency with which ' $m$ ' should be revolved so that ' $M$ ' remains stationary is ( $g =$ gravitational acceleration)

A body of mass 100 gram is tied to a spring of spring constant $8\text{ N/m}$, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed $8\text{ rad/s}$ then the ratio of extension in the spring to its natured length will be

A tube of length 1 m is filled completely with an ideal liquid of mass 2 M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\frac{F}{\alpha M}}$ in SI unit. The value of $\alpha$ is _________.

A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit radius is proportional to $(n)^x$. The value of $x$ is

A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with frequency 4 Hz. The acceleration of the particle in $\text{m/s}^2$ is

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9\text{ m}$ and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $\text{m/s}^2$):

A particle is moving in a circle with uniform speed. It has constant

For a particle in uniform circular motion

If the radius of curvature of the path of two particles of same mass are in the ratio $3 : 4$, then in order to have constant centripetal force, their velocities will be in the ratio of:

A particle of mass ' $m$ ' is performing uniform circular motion along a circular path of radius ' $r$ '. Its angular momentum about the axis passing through the centre and perpendicular to the plane is ' $L$ '. The kinetic energy of the particle is

A particle of mass ' $m$ ' performs uniform circular motion of radius ' $r$ ' with linear speed ' $v$ ' under the application of force ' $F$ '. If ' $m$ ', ' $v$ ' and $r$ ' are all increased by $20\%$ the necessary change in force required to maintain the particle in uniform circular motion, is

A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution.

If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $\theta$ is then given by:

A stone tied to $180\text{ cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x}\text{ m s}^{-2}$. The value of $x$ ________. (Take $\pi = \frac{22}{7}$)

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

A child of mass $5\text{ kg}$ is going round a merry-go-round that makes 1 rotation in $3.14\text{ s}$. The radius of the merry-go-round is $2\text{ m}$. The centrifugal force on the child will be

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $x = +2\text{ m}$, its velocity is $-4\hat{j}$ m/s. The object's velocity (v) and acceleration (a) at $x = -2\text{ m}$ will be

A body of mass 200 gram is tied to a spring of spring constant $12.5\text{ N/m}$, while other end of spring is fixed at point '$O$'. If the body moves about '$O$' in a circular path on a smooth horizontal surface with constant angular speed $5\text{ rad/s}$ then the ratio of extension in the spring to its natural length will be

A small block of mass $100\text{ g}$ is tied to a spring of spring constant $7.5\text{ N/m}$ and length $20\text{ cm}$. 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 $5\text{ rad/s}$ about point $A$, then tension in the spring is -

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:

A stone is projected at angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for short time, then the radius of the circular path will be ( $g =$ acceleration due to gravity)

A body moving in a circular path with a constant speed has constant

For a particle in uniform circular motion, the acceleration$\vec{a}$at any point P(R, $\theta$) on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed):

Two bodies of masses '$m$' and '$3m$' are rotating in horizontal circles of radii '$r$' and ' $\frac{r}{3}$' respectively. The tangential speed of the body of mass '$m$' is $n$ times that of the heavier body; while the centripetal force is same for both. The value of $n$ is

A mass of $0.5\text{ kg}$ is attached to one end of a massless spring whose natural length is $1\text{ m}$ and spring constant is $800\text{ N/m}$ The other end of the spring is fixed while the mass moves in a circular path in a horizontal plane with an angular speed of $20\text{ rad/s}$. The extension in the length of the spring will be:

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

A particle is moving along the circular path with constant speed and centripetal acceleration 'a'. If the speed is doubled, the ratio of its acceleration after and before the change is

A particle is performing U.C.M. along the circumference of a circle of diameter $50\text{ cm}$ with frequency $2\text{ Hz}$. The acceleration of the particle in $\text{m/s}^2$ is

A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is:

A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $\frac{V}{2}$ and radius is increased to '3r'. For this change, initial centripetal force needs to be

A particle moves in a circular orbit of radius '$r$' under a central attractive force, $F = -\frac{k}{r}$, where $k$ is a constant. The periodic time of its motion is proportional to

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by:

A projectile is thrown with an initial velocity $(a\hat{i} + b\hat{j})\text{ m/s}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then

A particle of mass m moves in a circular orbit under the central potential field, $U(r) = -\frac{C}{r}$, where C is a positive constant. The correct radius $-$ velocity graph of the particle's motion is:

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of:

A particle of mass $m$ is performing UCM along a circle of radius $r$. The relation between centripetal acceleration $a$ and kinetic energy $E$ is given by

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $\ell$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in $\text{m/s}^2$ is

A body of mass $m$ is performing a UCM in a circle of radius $r$ with speed $v$. The work done by the centripetal force in moving it through $\left(\frac{2}{3}\right)\text{rd}$ of the circular path is

A mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now halved keeping the angular momentum same, the linear velocity is

The real force ' $F$ ' acting on a particle of mass $m$ ' performing circular motion acts along the radius of circle ' $r$ ' and is directed towards the centre of circle. The square root of magnitude of such force is ( $T =$ periodic time)

A body is projected at t = 0 with a velocity 10 ms–1 at an angle of 60o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms–2, the value of R is:

If a body moving in a circular path maintains constant speed of 10ms${}^{-1}$, then which of the following correctly describes relation between acceleration and radius?

A body of mass 'm' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, the elongation in the spring is 5 cm. The original length of the spring is:

Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

For a particle in uniform circular motion the acceleration$\vec{a}$at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?