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 →

MEDIUM

Earn 100

Derive the expression for maximum safety speed with which vehicle should move along a curved horizontal road. State the significance of it.

Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Circular Motion

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>Laws of Motion>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:

MEDIUM

Physics>Mechanics>Laws of Motion>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})

MEDIUM

Physics>Mechanics>Laws of Motion>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>Laws of Motion>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

MEDIUM

Physics>Mechanics>Laws of Motion>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

EASY

Physics>Mechanics>Laws of Motion>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?

EASY

Physics>Mechanics>Laws of Motion>Circular Motion

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>Laws of Motion>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 :

EASY

Physics>Mechanics>Laws of Motion>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}

MEDIUM

Physics>Mechanics>Laws of Motion>Circular Motion

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>Laws of Motion>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 _______

MEDIUM

Physics>Mechanics>Laws of Motion>Circular Motion

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>Laws of Motion>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)

EASY

Physics>Mechanics>Laws of Motion>Circular Motion

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>Laws of Motion>Circular Motion

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,

MEDIUM

Physics>Mechanics>Laws of Motion>Circular Motion

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

EASY

Physics>Mechanics>Laws of Motion>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}

]

MEDIUM

Physics>Mechanics>Laws of Motion>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>Laws of Motion>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?

Derive the expression for maximum safety speed with which vehicle should move along a curved horizontal road. State the significance of it.

Important Questions on Laws of Motion

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