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When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be

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Important Questions on Motion of System of Particles and Rigid Bodies

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A rigid massless rod of length $3 l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

Consider two uniform discs of the same thickness and different radii

R_{1} = R

and

R_{2} = α R

made of the same material. If the ratio of their moments of inertia

I_{1}

and

I_{2}

, respectively, about their axes is

I_{1} : I_{2} = 1 : 16

then the value of

α

is :

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $A B$ is (g-acceleration due to gravity)

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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

In the figure $A$ and $B$ are identical blocks, each of mass $m$ and $C$ is a circular disc of equal mass $m$ . Pulley is massless and ffictionless and thread is inextensible. Neglecting friction, find the acceleration of block $A$ and $B$ .
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HARD

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A body of mass

m

slides down an incline and reaches the bottom with a velocity.

v

. If the same mass were in the form of a ring which rolls down this incline. The velocity of the ring at the bottom would have been

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A rigid body is in pure rotation, that is undergoing fixed axis rotation. Then which of the following statements are true -

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A light thread has been tightly wrapped around a disc of mass $M$ and radius $R$ . The disc has been placed on a smooth table, lying flat as shown. The other end of the string has been attached to a mass $m$ as shown. The system is released from rest. Find the acceleration of the disc and block.
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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A uniform rod rotates in a vertical plane about the shown axis. Angular velocity at the moment is $ω$ . Then, force on the rod by the axis at the moment
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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.These axes need not be stationary.Consider,for example, a thin uniform disc welded (rigidly fixed ) horizontally at its rim to a massless stick,as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed ω,the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis,and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q).Both these motions have the same angular speed ω in this case

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Now consider two similar systems as shown in the figure : Case(a) the disc with its face vertical and parallel to x-z plane ; Case (b) the disc withits face making an angle of 45^o with x-y plane and its horizontal diameter parallel to x-axis.In both the cases,the disc is welded at point P, and the systems are rotated with constant angular speed ω about the z-axis.

Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct ?

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A uniform rod is hanging with the help of the unintelligible strings as shown. Then:

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

One end of a uniform rod of length l and mass is hinged at A. it is released from rest from horizontal position AB as shown in figure, The force exerted by the rod on the hinge when its becomes vertical is

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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

When a ceiling fan is switched off, its angular velocity fall to half while it makes 36 rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then its radius of gyration about a parallel axis through its centre of mass will be

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

Select the wrong statement -

Statement-I : A body may be in pure rotation under the action of single external force.

Statement-II : If a body is in pure rotation under action of single external force then it must not be rigid.

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A uniform rod of mass $M$ and length $l$ is suspended by two vertical inextensible strings as shown in figure. Calculate tension in left string at the instant, when right string snaps.
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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

The moment of inertia of a body about a given axis is

1.2 kg m^{2}

. Initially, the body is at rest. In order to produce rotational kinetic energy of

1500 J

, the angular acceleration of

25 rad s^{- 2}

must be applied about the axis for a duration of

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A weightless rod of length

l

carries two equal masses

m

one fixed at the end and other in the middle of the rod. The rod can revolve in a vertical plane about

A

. Then horizontal velocity which must be imparted to end

C

of the rod to deflect it to the horizontal position is

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down(no rolling) the plane. Then maximum acceleration down the plane is for

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

Cotyledons are also called-

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Bodies>Torque

A cord is wrapped on a pulley (disk) of mass M and radius R as shown in Figure. To one end of the cord, a block of mass M is connected as shown and to other end in (a) a force of 2 Mg and in (b) a block of mass 2M. Let angular acceleration of the disk in A and B is

α_{A}

and

α_{B}

respectively, then (cord is not slipping on the pulley)

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When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be

Important Questions on Motion of System of Particles and Rigid Bodies

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