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 force is a net force that acts on an object to keep moving along a circular path.

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Important Questions on Circular Motion

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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)

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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 $(v)$ ?

Question Image

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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})

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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,

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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})

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

Science>Physics>Circular Motion>Tangential and Radial Acceleration

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

MEDIUM

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A disc of radius

R

has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length R attached to its other end as shown in figure. The disc is rotated with a constant angular velocity

ω

. The string is making an angle

45 °

with the rod. Then the angular velocity

ω

of disc is

Question Image

EASY

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A stone of mass $0.3 kg$ , attached to a $1.5 m$ long string, is whirled around in a horizontal circle on a frictionless table, at a speed of $6 m s^{- 1}$ . The tension in the string is

HARD

Science>Physics>Circular Motion>Tangential and Radial Acceleration

A particle of mass

m

is rotating in a horizontal circle of radius

R

and is attached to a hanging mass

M

, as shown in the figure. The speed of rotation required by the mass

m

to keep

M

steady is

A force is a net force that acts on an object to keep moving along a circular path.

Important Questions on Circular Motion

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