The position vector of a particle R → as a function of time is given by: R → = 4 sin ⁡ 2 π t i ^ + 4 c o s ⁡ ( 2 π t ) j ^ Where R is in meters, t is in seconds and i ^ and j ^ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

Magnitude of the velocity of particle is 8 meter/second

Magnitude of acceleration vector is v 2 R , where v is the velocity of particle

Patch of the particle is a circle of radius 4 meter

Acceleration vector is along - R →

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Important Questions on Circular Motion

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

One end of massless spring of spring constant

100 N / m

and natural length

0.49 m

is fixed and other end is connected to a body of mass

0.5 kg

lying on a frictionless horizontal table. The spring remains horizontal. If the body is made to rotate at an angular velocity of

2 rad / s,

then the elongation of the spring will be

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

The position vector of a particle

\vec{R}

as a function of time is given by:

\vec{R} = 4 \sin (2 π t) \hat{i} + 4 c o s (2 π t) \hat{j}

Where R is in meters, t is in seconds and

\hat{i}

and

\hat{j}

denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

If a particle of mass

m

is moving in a horizontal circle of radius

r

with a centripetal force

(- \frac{K}{r^{2}})

, total energy is

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

The Earth (of mass $6 \times 10^{24} kg$ ) revolves round the sun with an angular velocity of $2 \times 10^{- 7} rad s^{- 1}$ in a circular orbit of radius $1.5 \times 10^{11} km .$ The force exerted by the sun on the earth is

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

A pulley of radius

2 m

is rotated about its axis by a force

= (20 t - 5 t^{2})

newton (where

t

is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is

10 kg m^{2},

the number of rotation made by the pulley before its direction of motion is reversed is

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A particle is moving with uniform speed along the circumference of a circle of radius

R

under the action of a central fictitious force

F

which is inversely proportional to

R^{3}

. Its time period of revolution will be given by :

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

A uniform rod of length

l

and density

ρ

is revolving about a vertical axis passing through its one end. If

ω

is the angular velocity of the rod then the centrifugal force per unit area of the rod is

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$ . Which of the following curve represents the correct relation between the normal reaction on the block by the wall $(N)$ and speed of the block $(v)$ ?

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EASY

Physics>Mechanics>Circular Motion>Banking of Roads

One end of a string of length

' l'

is connected to a particle of mass

' m'

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

' v'

, the net force on the particle (directed towards the centre is: (

T

is the tension in the string)

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

Two spheres of equal masses are attached to a string of length $2 m$ as shown in figure. The string and the sphere are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio?
$\frac{(Tension in the string between P and Q)}{(Tension in the string between P and O)} =$ ?

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HARD

Physics>Mechanics>Circular Motion>Banking of Roads

Distinguish between centripetal and centrifugal force.

HARD

Physics>Mechanics>Circular Motion>Banking of Roads

A particle of mass

m

is fixed to one end of a light spring having force constant

k

and unstretched length

l .

The other end is fixed. The system is given an angular speed

ω

about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A circular disc rotates at

60

revolutions per minute about an axis passing through its center. A coin of

18 g

is placed at a distance of

8 cm

from the center of the disc. The centrifugal force on the coin is

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A small object placed on a rotating horizontal turn table just slips when it is placed at a distance of

4 cm

from the axis of rotation, if the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A boy ties a stone of mass

100 g

to the end of a

2 m

long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of

80 N

. If the maximum speed with which the stone can revolve is

\frac{K}{π} rev \min^{- 1}

. The value of

K

is :
(Assume the string is massless and un-stretchable)

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

A car is moving with a constant speed of

20 m s^{- 1}

in a circular horizontal track of radius

40 m

. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take

g = 10 m s^{- 2}

)

EASY

Physics>Mechanics>Circular Motion>Banking of Roads

A body of mass

200 g

is tied to a spring of spring constant

12.5 N m^{- 1}

, while the other end of spring is fixed at point

O

. If the body moves about

O

in a circular path on a smooth horizontal surface with constant angular speed

5 rad s^{- 1}

, then the ratio of extension in the spring to its natural length will be :

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

A simple pendulum is suspended from the ceiling of a car taking a turn of radius

10 m

at a speed of

10 m s^{- 1} .

Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. (Assume

g = 10 m s^{- 2}

)

MEDIUM

Physics>Mechanics>Circular Motion>Banking of Roads

An insect is at the bottom of a hemispherical ditch of radius

1 m

. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is

0.75,

then

h

: (g = 10 m s^{- 2})

HARD

Physics>Mechanics>Circular Motion>Banking of Roads

A smooth wire of length

2 π r

is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed

ω

about the vertical diameter

A B,

as shown in figure, the bead is at rest with respect to the circular ring at position

P

as shown. Then the value of

ω^{2}

is equal to:
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Important Questions on Circular Motion

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