EASY

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A uniform rectangular box of dimensions $(40 cm \times 20 cm)$ is kept on a horizontal smooth surface at a distance $10 m$ from a wall. A constant force $F$ has to applied horizontally at the highest point as shown. The minimum time (in seconds) to reach the wall without causing the box to rotate is

Important Questions on Systems of Particles and Rotational Motion

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid cylinder of mass

50 k g

and radius

0.5 m

is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of

2

revolutions

s^{- 2}

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A rope is wound around a hollow cylinder of mass

3 kg

and radius

40 cm.

What is the angular acceleration of the cylinder if the rope is pulled with a force of

30 N

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A solid cylinder of mass

2 k g

and radius

4 c m

is rotating about its axis at the rate of

3 rpm

. The torque required to stop after

2 π

revolutions is

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height $a (a < R)$ by applying a force $F$ at its centre $' O'$ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $F$ required is:

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HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

An automobile moves on a road with a speed of

54 k m h^{- 1}

. The radius of its wheels is

0.45 m

and the moment of inertia of the wheel about its axis of rotation is

3 k g m^{2}

. If the vehicle is brought to rest in

15 s

, the magnitude of average torque transmitted by its brakes to the wheel is:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle of mass

m

is moving along a trajectory given by

x = x_{0} + a c o s ω_{1} t

y = y_{0} + b s i n ω_{2} t

The torque, acting on the particle about the origin, at

t = 0

is:

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A wheel of radius

R

and mass

M

is placed at the bottom of a fixed step of height

R

as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque

τ

about an axis normal to the plane of the paper passing through the point

Q

. Which of the following options is/are correct?

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EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A force $\vec{F} = 4 \hat{i} + 3 \hat{j} + 4 \hat{k}$ is applied on an intersection point of $x = 2$ plane and $x$ -axis. The magnitude of torque of this force about a point $(2, 3, 4)$ is ________.

(Round off to the Nearest Integer)

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A slender uniform rod of mass

M

and length

l

is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle

θ

with the vertical is:

Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A uniform bar of mass $M$ is supported by a pivot at its top about which the bar can swing like a pendulum. If a force $F$ is applied perpendicular to the lower end of the bar as shown in figure, what is the value of $F$ in order to hold the bar in equilibrium at an angle $(θ)$ from the vertical

Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

Find the torque about the origin when a force of

3 \hat{j} N

acts on a particle whose position vector is

2 \hat{k} m

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

To mop-clean a floor, a cleaning machine presses a circular mop of radius

R

vertically down with a total force

F

and rotates it with a constant angular speed about its axis. If the force

F

is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is

μ,

the torque, applied by the machine on the mop is:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A light rope is wound around a hollow cylinder of mass

4 kg

and radius

40 cm

. If the rope is pulled with a force of

40 N

, its angular acceleration is______.

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A metal coin of mass

5 g

and radius

1 c m

is fixed to a thin stick

A B

of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about

A B

25

rotations per second in

5 s

, is close to:
Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

Consider a $20 kg$ uniform circular disk of radius $0.2 m$ . It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F = 20 N$ through a massless string wrapped around its periphery as shown in the figure.

Question Image

Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50 rad s^{- 1}$ . The value of $n$ , to the nearest integer, is _______ .

[Given : In one complete revolution, the disk rotates by $6.28 rad$ ]

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle of mass

M = 0.2 kg

is initially at rest in the

x y

-plane at a point

(x = - l, y = - h)

, where

l = 10 m

and

h = 1 m

. The particle is accelerated at time

t = 0

with a constant acceleration

a = 10 m s^{- 2}

along the positive

x

-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by

\vec{L}

and

\vec{τ}

, respectively.

\hat{i}, \hat{j}

and

\hat{k}

are unit vectors along the positive

x, y

and

z

-directions, respectively. If

\hat{k} = \hat{i} \times \hat{j}

then which of the following statement(s) is (are) correct?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A rigid body of mass $M$ and radius $R$ rolls without slipping on an inclined plane of inclination $θ,$ under gravity. Match the type of body Column I with magnitude of the force of friction Column II.

Column I		Column II
A)	For ring	I)	$\frac{M g \sin θ}{2.5}$
B)	For solid sphere	II)	$\frac{M g \sin θ}{3}$
C)	For solid cylinder	III)	$\frac{M g \sin θ}{3.5}$
D)	For hallow cylinder	IV)	$\frac{M g \sin θ}{2}$

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A wheel of radius, $R$ with an axle of radius, $\frac{R}{2}$ is as shown in the figure and is free to rotate about a frictionless axis through its center and perpendicular to the page. Three forces $(F, F, 2 F)$ , are exerted tangentially to the respective rims as shown in the figure.

Question Image

The magnitude of the net torque acting on the system is nearly,

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

Consider a body of mass

1.0 kg

at rest at the origin at time

t = 0

. A force

\vec{F} = (α t \hat{i} + β \hat{j})

is applied on the body, where

α = 1.0 {Ns}^{- 1}

and

β = 1.0 N

. The torque acting on the body about the origin at time

= 1.0 s

\vec{τ}

. Which of the following statements is (are) true?

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Torque

A particle of mass

20 g

is released with an initial velocity

5 m s^{- 1}

along the curve from the point

A,

as shown in the figure. The point

A

is at height

h

from point

B .

The particle slides along the frictionless surface. When the particle reaches point

B,

its angular momentum about

O

will be: (Take

g = 10 m s^{- 2}

)

A uniform rectangular box of dimensions (40 cm × 20 cm) is kept on a horizontal smooth surface at a distance 10 m from a wall. A constant force F has to applied horizontally at the highest point as shown. The minimum time (in seconds) to reach the wall without causing the box to rotate is

Important Questions on Systems of Particles and Rotational Motion

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