Circular Motion

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

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 pa...

For a particle in uniform circular motion

A particle rotates in a horizontal circle of radius 'R' in a conical funnel with constant speed 'V'. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (g-acceleration due to gr...

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 $' \mathrm{r}$ ' are all increased by $20 \%$ the necessary change in fo...

A particle at rest starts moving with constant angular acceleration \(4 ~\mathrm{rad} / \mathrm{s}^2\) in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

A simple pendulum of length \(2 \mathrm{~m}\) is given a horizontal push through angular displacement of \(60^{\circ}\). If the mass of bob is 200 gram, the angular velocity of the bob will be (Take Acceleration due to gravity $$=10 \mathrm...

A particle of mass '\(\mathrm{m}\)' moves along a circle of radius '\(r\)' with constant tangential acceleration. If K.E. of the particle is '\(E\)' by the end of third revolution after beginning of the motion, then magnitude of tangential ...

A string of length '\(L\)' fixed at one end carries a body of mass '\(\mathrm{m}\)' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string mak...

On dry road, the maximum speed of a vehicle along a circular path is '\(V\)'. When the road becomes wet, maximum speed becomes \(\frac{\mathrm{V}}{2}\). If coefficient of friction of dry road is '\(\mu\)' then that of wet road is

A particle moves around a circular path of radius '\(r\)' with uniform speed '\(V\)'. After moving half the circle, the average acceleration of the particle is

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)

Two particles having mass '\(M\)' and '\(m\)' are moving in a circular path with radius '\(R\)' and '\(r\)' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second part...

A railway track is banked for a speed ',\(v\)' by elevating outer rail by a height '\(h\)' above the inner rail. The distance between two rails is 'd' then the radius of curvature of track is ( \(\mathrm{g}=\) gravitational acceleration)

A body of mass '\(\mathrm{m}\)' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ( \(\mathrm{g}\) = gravitational acceleration)

A particle is moving in a circle with uniform speed '\(v\)'. In moving from a point to another diametrically opposite point

A ball of mass '\(\mathrm{m}\)' is attached to the free end of a string of length '\(l\)'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram.
The angular velocity '\(\omega\)' of the ball will be...

In a conical pendulum the bob of mass '\(\mathrm{m}\)' moves in a horizontal circle of radius '\(r\)' with uniform speed '\(\mathrm{V}\)'. The string of length '\(\mathrm{L}\)' describes a cone of semi vertical angle '\(\theta\)'. The centr...

A body of mass 200 gram is tied to a spring of spring constant \(12.5 \mathrm{~N} / \mathrm{m}\), 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 co...

A particle performing uniform circular motion of radius \(\frac{\pi}{2} \mathrm{~m}\) makes '\(\mathrm{x}\)' revolutions in time '\(t\)'. Its tangential velocity is

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

A bucket containing water is revolved in a vertical circle of radius \(r\). To prevent the water from falling down, the minimum frequency of revolution required is (\(\mathrm{g}=\) acceleration due to gravity)

Two bodies of masses '\(\mathrm{m}\)' and '\(3 \mathrm{~m}\)' are rotating in horizontal speed of the body of mass '\(m\)' is \(n\) times that of the value of heavier body; while the centripetal force is same for both. The value of \(n\) is

A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [\(\mathrm{g}=\) acceleration due to gravity]

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 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 \(50 \mathrm{~cm}\) with frequency \(2 \mathrm{~Hz}\). The acceleration of the particle in \(\mathrm{m} / \mathrm{s}^2\) is

A projectile is thrown with an initial velocity \((a \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}\), where \(\hat{i}\) and \(\hat{j}\) are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is t...

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

The angular displacement of body performing circular motion is given by \(\theta=5 \sin \frac{\pi t}{6}\). The angular velocity of the body at \(t=3\) second will be \(\left[\sin \frac{\pi}{2}=1, \cos \frac{\pi}{2}=0\right]\)

If \(\omega_1\) is angular velocity of hour hand of clock and \(\omega_2\) is angular velocity of the earth, then the ratio \(\omega_1\) : \(\omega_2\) is

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

The angle of banking '\(\theta\)' for a meter gauge railway line is given by \(\theta=\tan ^{-1}\left(\frac{1}{20}\right)\). What is the elevation of the outer rail above the inner rail?

A particle at rest starts moving with a constant angular acceleration of \(4 \mathrm{~rad} / \mathrm{s}^2\) in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After time $t$ he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the groun...

A body is moving along a circular track of radius 100 m with velocity $20 \mathrm{~m} / \mathrm{s}$. Its tangential acceleration is $3 \mathrm{~m} / \mathrm{s}^2$, then its resultant acceleration will be

A particle is moving in a radius \(R\) with constant speed \(v\). The magnitude of average acceleration after half revolution is

In non-uniform circular motion, the ratio of tangential to radial acceleration is (\(r=\) radius, \(\alpha=\) angular acceleration and \(v=\) linear velocity)

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 starting from rest moves along the circumference of a circle of radius \(r\) with angular acceleration \(\alpha\). The magnitude of the average velocity, in the time it completes the small angular displacement \(\theta\) 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

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 $\left(\frac{2}{3}\right) \mathrm{rd}$ of the circular path is

A stone of mass 1 kg is tied to a string 2 m long and it's rotated at constant speed of $40 \mathrm{~ms}^{-1}$ in a vertical circle. The ratio of the tension at the top and the bottom is [Take $g=10 \mathrm{~ms}^{-2}$]

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)

In U.C.M., when time interval $\delta t \rightarrow 0$, the angle between change in velocity ( $\delta \mathbf{v}$ ) and linear velocity $(\boldsymbol{v})$ will be

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 $\mathrm{m} / \mathrm{s}^2$ is