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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A gramophone disc is set revolving in a horizontal plane and reaches a steady state of motion of two revolutions per second. It is found that a small coin placed on the disc will remain there if its centre is not more than $5 cm$ from the axis of rotation. The coefficient of friction between the coin and the disc is

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Important Questions on Circular Motion

EASY

Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

A curved road of diameter

1.8 km

is banked so that no friction is required at a speed of

30 m s^{- 1}

. What is the banking angle?

EASY

Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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?

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Physics>Mechanics>Circular Motion>Dynamics of 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})

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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})

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

A disc with a flat small bottom beaker placed on it at a distance

R

from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity

ω

. The coefficient of static friction between the bottom of the beaker and the surface of the disc is

μ

. The beaker will revolve with the disc if :

HARD

Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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>Dynamics of 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,

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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}

)

EASY

Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

A curved in a level road has a radius

75 m

. The maximum speed of a car turning this curved road can be

30 m s^{- 1}

without skidding. If radius of curved road is changed to

48 m

and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____

m s^{- 1}

EASY

Physics>Mechanics>Circular Motion>Dynamics of 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}

]

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

A point mass

m

is moved in a vertical circle of the radius

r

with the help of a string. The velocity of the mass is

\sqrt{7 g r}

at the lowest point. The tension in the string at the lowest point is:

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Physics>Mechanics>Circular Motion>Dynamics of 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>Circular Motion>Dynamics of Circular Motion

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)

HARD

Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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:
Question Image

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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?
$\frac{(Tension in the string between P and Q)}{(Tension in the string between P and O)} =$ ?

Question Image

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

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>Dynamics of Circular Motion

A mass

m

is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is

1 cm

. If the angular speed is doubled, the elongation in the spring is

6 cm

. The original length of the spring is

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Physics>Mechanics>Circular Motion>Dynamics of Circular Motion

A coin placed on a rotating table just slips when it is placed at a distance of

1 cm

from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre:

EASY

Physics>Mechanics>Circular Motion>Dynamics of 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>Circular Motion>Dynamics of Circular Motion

A cycle turns around a curve at

25

miles per hour. If he turns at double the speed, the tendency to overturn is _______

Important Questions on Circular Motion

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