HARD

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Consider a disc rotating in the horizontal plane with a constant angular speed ω about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $\frac{1}{8}$ rotation,(ii) their range is less than half the disc radius,and (iii) ω remains constant throughout. Then

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Important Questions on Motion in a Plane

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A particle is performing uniform circular motion along the circumference of a circle of diameter

50 cm

with frequency

2 Hz

. The acceleration of the particle in

m s^{- 2}

is:

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the

n^{t h}

power of R. If the period of rotation of the particle is T, then:

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A uniform rod of length

l

is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is

T (x)

at a distance

x

from the axis, then which of the following graphs depicts it most closely?

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A train is moving towards north. At one place it turns towards north-east. Here, we observe that:

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

In the given figure, $a = 15 m s^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of the radius $R = 2 .5 m$ at a given instant of time. The speed of the particle is

Question Image

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A clock has a continuously moving second's hand of $0.1 m$ length. The average acceleration of the tip of the hand (in units of $m s^{- 2}$ ) is of the order of :

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A particle is moving in a circular path of radius a under the action of an attractive potential

U = - \frac{k}{2 r^{2}} .

Its total energy is:

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

An object moves along the circle with normal acceleration proportional to

t^{α}

, where

t

is the time and is

α

a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

Two cars

S_{1}

and

S_{2}

are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution

3 \min

and

24 \min

, respectively. At the time

t = 0,

the cars are the farthest apart. Then, the two cars will be,

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A car goes around uniform circular track of radius

R

at a uniform speed

v

once in every

T

seconds. The magnitude of the centripetal acceleration is

a_{c}

. If the car now goes uniformly around a larger circular track of radius

2 R

and experiences a centripetal acceleration of magnitude

8 a_{c}

. Then, its time period is

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A body moving along a circular path due to a centripetal force having constant magnitude is an example of motion with ___ .

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

If a body moving in a circular path maintains constant speed of

10 m s^{- 1}

, then which of the following correctly describes the relation between acceleration and radius?

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A solid body rotates with angular velocity

ω = a t \hat{i} + b t^{2} \hat{j}

where

a = 1 rad s^{- 2}

and

b = 0.5 rad s^{- 3}

and

t

is in seconds. Calculate the angle between the vectors of the angular velocity and the angular acceleration at

t = 1 \sec

HARD

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A particle moves such that its position vector

\vec{r} (t) = \cos ω t \hat{i} + \sin ω t \hat{j}

, where

ω

is a constant and

t

is time. Then which of the following statements is true for the velocity

\vec{v} (t)

and acceleration

\vec{a} (t)

of the particle:

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A particle performing

U . C . M .

of radius

\frac{π}{2} m

makes

x

revolutions in time

t

. Its tangential velocity is

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A uniform rod of mass

0.5 kg

and length

0.5 m

is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is (Acceleration due to gravity

= 10 m s^{- 2}

)

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

Two cars of masses

m_{1}

, and

m_{2}

are moving in the circles of radii

r_{1}

and

r_{2}

respectively. Their angular speeds

{}^{'}ω_{1}^{'}

and

{}^{'}ω_{2}^{'}

are such that they both complete one revolution in the same time

t

. The ratio of linear speed of

m_{1}

' to the linear speed of

m_{2}

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

One end of string of length

l

is connected to a particle of mass

m

and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed

v

, the net force on the particle (directed towards center) will be (

T

represents the tension in the string)

MEDIUM

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

A mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_{0}$ at a radius $R_{0}$ . The mass is attached to a string which passes through a smooth hole in plane as shown.

Question Image

The tension in the string is increased gradually and finally $m$ moves in a circle of radius $\frac{R_{0}}{2}$ . The final value of the kinetic energy is:

EASY

Physics>Mechanics>Motion in a Plane>Uniform Circular Motion

If the kinetic energy of a particle of mass $m,$ performing uniform circular motion in a circle of radius $r,$ is $E,$ find the acceleration of the particle.

Important Questions on Motion in a Plane

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