Circular Motion - Mechanics - Physics Previous Year Questions

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

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 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)

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 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 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 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 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 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 ground is

[g = acceleration due to gravity]

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 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?

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 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 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 body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration 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 twice the maximum height reached by it, then

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