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Which of the following correctly describes the centripetal acceleration vector for a particle moving with uniform speed in a circular path?

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Important Questions on Motion in a Plane

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

A thin metallic disc is rotating with constant angular velocity about a vertical axis that is perpendicular to its plane and passes through its centre. The rotation causes the free electrons in the disc to redistribute. Assume that, there is no external electric or magnetic field. Then,

EASY

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

A particle performing

U . C . M .

of radius

\frac{π}{2} m

makes

x

revolutions in time

t

. Its tangential velocity is

MEDIUM

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

A uniform rod of mass

0.5 kg

and length

0.5 m

is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is (Acceleration due to gravity

= 10 m s^{- 2}

)

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.

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)

EASY

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

A particle is moving in uniform circular motion with speed

v

and radius

R

. The angular acceleration of the particle is:

EASY

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

Two cars of masses

m_{1}

, and

m_{2}

are moving in the circles of radii

r_{1}

and

r_{2}

respectively. Their angular speeds

{}^{'}ω_{1}^{'}

and

{}^{'}ω_{2}^{'}

are such that they both complete one revolution in the same time

t

. The ratio of linear speed of

m_{1}

' to the linear speed of

m_{2}

EASY

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

If a particle moves in a curved path, it must have a component of acceleration

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 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

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

A block of

200 g

mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius

20 cm

. If the block takes

40 s

to complete one round, the normal force by the side walls of the groove is:

MEDIUM

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

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:

MEDIUM

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

A bead is tied on one end of a stiff rope of length

1 m .

With the other end of the rope as the center, the rope is rotated in such a way that the bead completes

10

revolutions per second. The centripetal acceleration of the bead is

EASY

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

A scooter is going round a circular road of radius

200 m

at a speed of

20 m s^{- 1}

. The angular speed of scooter will be

EASY

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

A body rotating with an angular speed of

600 rpm

is uniformly accelerated to

1800 rpm

10 \sec .

The number of rotations made in the process is

EASY

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

The centripetal acceleration required for a particle to move on a circle of radius

r

with speed

v

EASY

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

The angular velocity of a ceiling fan reduces to

50 %

after

36

rotations since it is switched off. Assuming uniform retardation, the number of rotations it further makes before coming to rest is

EASY

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

A train is moving towards north. At one place it turns towards north-east. Here, we observe that:

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

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?

Which of the following correctly describes the centripetal acceleration vector for a particle moving with uniform speed in a circular path?

Important Questions on Motion in a Plane

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