EASY

Earn 100

Torque acting on the body is the product of force and perpendicular distance between the axis of and line of action of force.

100% studentsanswered this correctly

Important Questions on Systems of Particles and Rotational Motion

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

A uniform wooden stick of mass

1.6 kg

and length

l

rests in an inclined manner on a smooth, vertical wall of height h

(< l)

such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of

30^{o}

with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio

\frac{h}{l}

and the frictional force

f

at the bottom of the stick are:

(g = 10 m s^{- 2})

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

A uniform rod of length $l$ and mass $m$ is free to rotate in a vertical plane about $A$ . The rod initially in horizontal position is released. The initial angular acceleration of the rod is (Moment of inertia of rod about $A$ is $\frac{m l^{2}}{3}$ )

Question Image

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

In a physical balance working on the principle of moments, when

5 mg

weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

The disc of mass $M$ with uniform surface mass density $σ$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $(\frac{x a}{3 π}, \frac{x a}{3 π})$ where $x$ is _______ . (Round off to the Nearest Integer) [ $a$ is an area as shown in the figure]

Question Image

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

A uniform rod

A B

is suspended from a point

X

, at a variable distance

x

from

A

, as shown. To make the rod horizontal, a mass

m

is suspended from its end

A

. A set of

(m, x)

value is recorded. The appropriate variables that give a straight line, when plotted, are:

Question Image

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

L

-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If

A B = B C,

and the angle made by

A B

with downward vertical is

θ,

then:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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>Equilibrium of a Rigid Body

A square loop of side

2 a

and carrying current

I

is kept in

xz

plane with its centre at origin. A long wire carrying the same current

I

is placed parallel to

z

-axis and passing through point

(0, b, 0), (b > > a)

. The magnitude of torque on the loop about

z

-axis will be :

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

Torque per unit moment of inertia is equal to

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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>Equilibrium of a Rigid Body

If force

\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}

acts on a particle having position vector

2 \hat{i} + \hat{j} + 2 \hat{k}

then, the torque about the origin will be:

EASY

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

Point masses $m_{1}$ and $m_{2}$ are placed at the opposite ends of rigid rod of length $L$ , and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $L$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $ω_{0}$ is minimum, is given by:
Question Image

HARD

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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?

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

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:

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

A mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$ . If the string does not slip on the cylinder, then with what acceleration will the mass release? (Assume $g =$ acceleration due to gravity)

Question Image

MEDIUM

Physics>Mechanics>Systems of Particles and Rotational Motion>Equilibrium of a Rigid Body

Define couple. State the SI unit of moment of couple.

Torque acting on the body is the product of force and perpendicular distance between the axis of and line of action of force.

Important Questions on Systems of Particles and Rotational Motion

Learn and Prepare for any exam you want !