Circular Motion - Mechanics - Physics Previous Year Questions

A car is travelling with linear velocity $v$ on a circular road of radius $r$. If its velocity is increasing at a rate of $a \mathrm{~ms}^{-2}$, then the resultant acceleration will be

If the radii of circular path of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be

A point $P$ is moving in uniform circular motion with radius 3 m . Let at some instant the acceleration of the point is $\quad \mathbf{a}=(6 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$, the position vector is $\mathbf{r}$ and velocity vector is $\mathbf{v}$. Choose the correct statement.

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

A body of mass $m$ slides down along a frictionless inclined plane from height $h$ and just completes motion in a vertical circle of radius 2 m after reaching the bottom. What is the value of $h$ ? [Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A merry-go-round rotating at a constant angular speed completes 9 rotations is 18 s . What is its angular speed?

A spherical bob of mass 250 g is attached to the end of a string having length 50 cm . The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is 72 N . The maximum possible value of angular velocity of bob (in $\mathrm{rad} / \mathrm{s}$ ) is

A cyclist is riding with a speed of $36 \mathrm{~km} / \mathrm{h}$. As he approaches a circular turn on the road of radius 50 m , he applies brakes and reduces his speed at the constant rate of $0.5 \mathrm{~m} / \mathrm{s}$ every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively, are

A circular freeway entrance and exit are commonly banked to control a moving car at $14 \mathrm{~m} / \mathrm{s}$. To design similar ramp for $28 \mathrm{~m} / \mathrm{s}$ one should

A cyclist leans with the horizontal at angle $30^{\circ}$, while negotiating round a circular road of radius $20 \sqrt{3} \mathrm{~m}$. The speed of the cycle should be

Consider a particle is moving with a minimum speed $v$ at highest point of vertical circle of radius $R$. If the radius of the circle doubled the corresponding minimum speed will be

Assume proton is rotating along a circular path of radius 1 m under a centrifugal force of $4 \times 10^{-12} \mathrm{~N}$. If the mass of proton is $1.6 \times 10^{-27} \mathrm{~kg}$, then its angular velocity of rotation is