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 →

EASY

Earn 100

An astronaut is orbiting the earth in a Space Station. Draw diagram to show the force exerted by the Earth on the astronaut and on the Space Station. Include the Earth on your diagram. Label each Arrow with the name of the force.

Important Questions on Rotational Dynamics

MEDIUM

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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

HARD

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

Distinguish between centripetal and centrifugal force.

HARD

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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>Rotational Dynamics>Centripetal and Centrifugal Forces

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

An astronaut is orbiting the earth in a Space Station. Draw diagram to show the force exerted by the Earth on the astronaut and on the Space Station. Include the Earth on your diagram. Label each Arrow with the name of the force.

Important Questions on Rotational Dynamics

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