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Arjun wants to lift the rock as shown in the figure. At which point should he apply the force so that he could lift the rock easily?

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Important Questions on Matter

MEDIUM

Physics>Mechanics>Matter>Simple Machines

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:

MEDIUM

Physics>Mechanics>Matter>Simple Machines

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

MEDIUM

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

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>Matter>Simple Machines

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

MEDIUM

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

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>Matter>Simple Machines

Torque per unit moment of inertia is equal to

EASY

Physics>Mechanics>Matter>Simple Machines

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?

EASY

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

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

HARD

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

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

HARD

Physics>Mechanics>Matter>Simple Machines

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:

Question Image

EASY

Physics>Mechanics>Matter>Simple Machines

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______.

EASY

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

The dimensional formula

[{ML}^{2} T^{- 2}]

represents

HARD

Physics>Mechanics>Matter>Simple Machines

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?

Question Image

HARD

Physics>Mechanics>Matter>Simple Machines

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>Matter>Simple Machines

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:

Arjun wants to lift the rock as shown in the figure. At which point should he apply the force so that he could lift the rock easily? Enable GingerCannot connect to Ginger Check your internet connection or reload the browserDisable in this text fieldEditEdit in GingerEdit in Ginger×

Important Questions on Matter

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Arjun wants to lift the rock as shown in the figure. At which point should he apply the force so that he could lift the rock easily?

Enable GingerCannot connect to Ginger Check your internet connection
or reload the browserDisable in this text fieldEditEdit in GingerEdit in Ginger×