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

Show that the angle of banking is independent of mass of vehicle.

Important Questions on Motion of System of Particles and Rigid Body

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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})

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v .$ If the coefficient of static friction between the tyres and the track is $μ_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is:

Question Image

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A cycle turns around a curve at

25

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

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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 $(v)$ ?

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

Statement I: A cyclist is moving on an unbanked road with a speed of $7 km h^{- 1}$ and takes a sharp circular turn along a path of the radius of $2 m$ without reducing the speed. The static friction coefficient is $0.2$ . The cyclist will not slip and pass the curve $(g = 9.8 m s^{- 2})$

Statement II : If the road is banked at an angle of $45 °$ , cyclist can cross the curve of $2 m$ radius with the speed of $18.5 km h^{- 1}$ without slipping. In the light of the above statements, choose the correct answer from the options given below.

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

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?

Show that the angle of banking is independent of mass of vehicle.

Important Questions on Motion of System of Particles and Rigid Body

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