EASY

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The time period of conical pendulum is given by

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Important Questions on Motion in a Plane

MEDIUM

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

The potential energy of a particle of mass m at a distance r from a fixed point O is given by

V (r) = k r^{2} / 2

, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true?

EASY

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

A car moves at a speed of

36 {kmh}^{- 1}

on a level road. The coefficient of friction between the car tyres and the road is

0.8

. The car negotiates a curve of radius

R

. If

g = 10 {ms}^{- 2}

, the car will skid (or slip) while negotiating the curve, if the value of

R

EASY

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

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.

MEDIUM

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

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

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

A particle of mass

m

is suspended from a ceiling through a string of length

L

. The particle moves in a horizontal circle of radius

r

such that

r = \frac{L}{\sqrt{2}}

. The speed of particle will be :

MEDIUM

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

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?

EASY

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

A car is moving on a horizontal curved road with radius

50 m

. The approximate maximum speed of car will be, if friction between tyres and road is

0.34

. [Take

g = 10 m s^{- 2}

]

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:

MEDIUM

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

A spherical bob hangs from a light inextensible string and moves in a horizontal circle with string making angle

θ

with the vertical. The length

l

of the string is then very slowly increased so that the motion is circular at all times to a good approximation. If

h

is the height from center of the circle to the pivot and

r

is the radius of the circle then

h \propto r^{a}

. The value of

a

EASY

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

A car is moving in a circular horizontal track of radius

10 m

with a constant speed of

10 m s^{- 1}

. A bob is suspended from the roof of the car by a light wire of length

1.0 m

. The angle made by the wire with the vertical is (in radian)

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,

MEDIUM

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

A disc of radius

0.4 m

and mass

1 kg

rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is

10 rad / s^{2} .

The tangential force applied to the rim of the disc is

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

Two stones of masses $m$ and $2 m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$ . The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is,

EASY

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

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)

MEDIUM

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

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

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:

MEDIUM

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

A car moves on a horizontal circular road of the radius,

16 m

with the increasing speed at a constant rate of

3 m s^{- 2} .

If the coefficient of friction between the road and tyre is

0.5,

then the minimum speed at which the car will skid is (assume

g = 10 m s^{- 2})

EASY

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

A car is moving in a circular path of radius

450 m

with a speed of

30 m s^{- 1}

. If the speed of the car is increased at a rate of

2 m s^{- 2}

, the resultant acceleration will be,

MEDIUM

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

A conical pendulum of length

l

makes an angle

θ = 45 °

with respect to

Z -

axis and moves in a circle in the

X Y

plane. The radius of the circle is

0.4 m

and its center is vertically below

O

. The speed of the pendulum, in its circular path, will be -

(T a k e g = 10 m s^{- 2})

The time period of conical pendulum is given by

Important Questions on Motion in a Plane

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