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

Derive an expression for the maximum speed of a vehicle along a curved path.

Important Questions on Rotational Dynamics

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

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

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

MEDIUM

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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 :

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

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

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

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

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

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}

)

HARD

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

Distinguish between centripetal and centrifugal force.

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 flat curve on a highway has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s. What is the minimum value of the coefficient of friction that will prevent the car from sliding?

(g = 9.8 m / s^{2})

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 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

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

EASY

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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)

MEDIUM

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

A ball of mass

m

is attached to the free end of an inextensible string of length

l

. Let

T

be the tension in the string. The ball is moving in horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be

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

MEDIUM

Physics>Mechanics>Rotational Dynamics>Centripetal and Centrifugal Forces

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})

Derive an expression for the maximum speed of a vehicle along a curved path.

Important Questions on Rotational Dynamics

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