MEDIUM

Earn 100

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad/s. Distance of the particle from axis is given by $R = R_{0} - β t$ where t stands for time. The speed of the particle as a function of time is

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Important Questions on Motion

EASY

Science>Physics>Motion>Angular Variables

If the kinetic energy of a particle of mass $m,$ performing uniform circular motion in a circle of radius $r,$ is $E,$ find the acceleration of the particle.

EASY

Science>Physics>Motion>Angular Variables

A car goes around uniform circular track of radius

R

at a uniform speed

v

once in every

T

seconds. The magnitude of the centripetal acceleration is

a_{c}

. If the car now goes uniformly around a larger circular track of radius

2 R

and experiences a centripetal acceleration of magnitude

8 a_{c}

. Then, its time period is

HARD

Science>Physics>Motion>Angular Variables

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the

n^{t h}

power of R. If the period of rotation of the particle is T, then:

MEDIUM

Science>Physics>Motion>Angular Variables

One end of a straight uniform

1 m

long bar is pivoted on horizontal table. It is released from rest when it makes an angle

30^{o}

from the horizontal (see figure). Its angular speed when it hits the table is given as

\sqrt{n} rad s^{- 1}

, where

n

is an integer. The value of

n

is ____________
Question Image

MEDIUM

Science>Physics>Motion>Angular Variables

A particle at a distance of

1 m

from the origin starts moving such that

\frac{d r}{d θ} = r,

where

(r, θ)

are polar coordinates. Then the angle between resultant velocity and tangential velocity component is:

EASY

Science>Physics>Motion>Angular Variables

Two particles

A

and

B

are moving in uniform circular motion in concentric circles of radii

r_{A}

and

r_{B}

with speed

v_{A}

and

v_{B}

, respectively. Their time period of rotation is the same. The ratio of angular speed of

A

to that of

B

will be,

EASY

Science>Physics>Motion>Angular Variables

One end of string of length

l

is connected to a particle of mass

m

and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed

v

, the net force on the particle (directed towards center) will be (

T

represents the tension in the string)

HARD

Science>Physics>Motion>Angular Variables

A particle moves such that its position vector

\vec{r} (t) = \cos ω t \hat{i} + \sin ω t \hat{j}

, where

ω

is a constant and

t

is time. Then which of the following statements is true for the velocity

\vec{v} (t)

and acceleration

\vec{a} (t)

of the particle:

EASY

Science>Physics>Motion>Angular Variables

A flywheel at rest is to reach an angular velocity of

24 rad s^{- 1}

8 s

with constant angular acceleration. The total angle turned through during this interval is

MEDIUM

Science>Physics>Motion>Angular Variables

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes

{(\frac{1}{4})}^{th}

of the original in time

t

and

n

revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)

EASY

Science>Physics>Motion>Angular Variables

Two particles $A, B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $ω .$ At $t = 0,$ their positions and direction of motion are shown in the figure:

Question Image

The relative velocity $\vec{V_{A}} - \vec{V_{B}}$ at $t = \frac{π}{2 ω}$ is given by:

MEDIUM

Science>Physics>Motion>Angular Variables

A mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_{0}$ at a radius $R_{0}$ . The mass is attached to a string which passes through a smooth hole in plane as shown.

Question Image

The tension in the string is increased gradually and finally $m$ moves in a circle of radius $\frac{R_{0}}{2}$ . The final value of the kinetic energy is:

HARD

Science>Physics>Motion>Angular Variables

A uniform rod of length

l

is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is

T (x)

at a distance

x

from the axis, then which of the following graphs depicts it most closely?

HARD

Science>Physics>Motion>Angular Variables

A particle is moving in a circular path of radius a under the action of an attractive potential

U = - \frac{k}{2 r^{2}} .

Its total energy is:

EASY

Science>Physics>Motion>Angular Variables

A particle is performing uniform circular motion along the circumference of a circle of diameter

50 cm

with frequency

2 Hz

. The acceleration of the particle in

m s^{- 2}

is:

EASY

Science>Physics>Motion>Angular Variables

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 $m s^{- 2}$ ) is of the order of :

EASY

Science>Physics>Motion>Angular Variables

A disc spinning at the rate

27.5

rad

s^{- 1}

is slowed at the rate 10 rad

s^{- 2}

. The time after which it will come to rest is

EASY

Science>Physics>Motion>Angular Variables

Two parallel discs are connected by a rigid rod of length $L = 0.5 m$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms is incident on one of the discs axially at different velocities $v$ , while the system is rotated at angular speed of, $600 rev s^{- 1}$ , so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in meter/second) of the atoms that will emerge at the other end.

Question Image

MEDIUM

Science>Physics>Motion>Angular Variables

In the given figure, $a = 15 m s^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of the radius $R = 2 .5 m$ at a given instant of time. The speed of the particle is

Question Image

MEDIUM

Science>Physics>Motion>Angular Variables

If a body moving in a circular path maintains constant speed of

10 m s^{- 1}

, then which of the following correctly describes the relation between acceleration and radius?

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad/s. Distance of the particle from axis is given by R=R0-βt where t stands for time. The speed of the particle as a function of time is

Important Questions on Motion

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