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Shown here are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to the right

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Important Questions on Motion in a Plane

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

In non-uniform circular motion, the ratio of tangential to radial acceleration is (

r =

radius of the circle,

u =

speed of the particle,

α =

angular acceleration)

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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:

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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:

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A wheel starting from rest gains an angular velocity of

10 rad s^{- 1}

after being uniformly accelerated for

5 \sec

. The total angle through which it has turned is

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

Two cars

S_{1}

and

S_{2}

are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution

3 \min

and

24 \min

, respectively. At the time

t = 0,

the cars are the farthest apart. Then, the two cars will be,

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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 :

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

The angular speed of the wheel of a vehicle is increased from,

360 rpm

1200 rpm

14 s

. Its angular acceleration is,

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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?

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A body moving along a circular path due to a centripetal force having constant magnitude is an example of motion with ___ .

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

An object moves along the circle with normal acceleration proportional to

t^{α}

, where

t

is the time and is

α

a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A solid body rotates with angular velocity

ω = a t \hat{i} + b t^{2} \hat{j}

where

a = 1 rad s^{- 2}

and

b = 0.5 rad s^{- 3}

and

t

is in seconds. Calculate the angle between the vectors of the angular velocity and the angular acceleration at

t = 1 \sec

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

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:

Shown here are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to the right

Important Questions on Motion in a Plane

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