JEE Questions for Physics Systems Of Particles And Rotational Motion Quiz 12 - MCQExams.com

As a part of a maintenance inspection the compressor of a jet engine is made to spin according to the graph as shown. The number of revolutions made by the compressor during the test is
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  • 9000
  • 16570
  • 12750
  • 11250
A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ω0. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform ω(t) will vary with time t as

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Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed ω. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by
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    Physics-Systems of Particles and Rotational Motion-89870.png

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The graph between the angular momentum L and angular velocity ω will be

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    Physics-Systems of Particles and Rotational Motion-89875.png

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The curve between loge L and loge P is (L is the angular momentum and P is the linear momentum)

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    Physics-Systems of Particles and Rotational Motion-89880.png

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    Physics-Systems of Particles and Rotational Motion-89886.png

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A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,
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A solid cylinder is rolling down a rough inclined plane of inclination θ. Then
  • The friction force is reduced if θ is reduced
  • The friction force is dissipative
  • The friction force is necessarily changing
  • The friction force will aid rotation but hinder translation

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The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is
where I1, I2, I3 and I4 are respectively moments of inertia about axes 1, 2, 3 and 4 which are in the plane of the plate.
Physics-Systems of Particles and Rotational Motion-89909.png
  • I1 + I2
  • I3 + I4
  • I1 + I3
  • I1 + I2 + I3 + I4
A uniform bar of length 6a and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal with speed 2v and v respectively, strike the bar (as shown in the fig.) and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by ω, E and vC respectively, we have after collision
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A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection, when the particle is at its maximum height h, is
  • Zero
  • 2)
    Physics-Systems of Particles and Rotational Motion-89917.png

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A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination θ. The coefficient of friction between the cylinder and incline is µ. Then
  • Frictional force is always µmg cos θ
  • Friction is dissipative force
  • By decreasing θ, frictional force decreases
  • Friction opposes translation and supports rotation
The figure shows a system consisting of (i) ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x–z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface
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Statement I If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass, remains constant.
Statement II The linear momentum of an isolated system remains constant.
  • Statement I is true, statement II is true ; statement II is a correct explanation for statement I
  • Statement I is true, statement II is true ; statement II is not a correct explanation for statement I
  • Statement I is true, statement II is false
  • Statement I is false, statement II is true
Statement I Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
Statement II By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
  • Statement I is true, statement II is true ; statement II is a correct explanation for statement I
  • Statement I is true, statement II is true ; statement II is not a correct explanation for statement I
  • Statement I is true, statement II is false
  • Statement I is false, statement II is true
Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2ω using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the direction.
The loss of kinetic energy during the above process is

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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2ω using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the direction.
When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

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    Physics-Systems of Particles and Rotational Motion-89934.png

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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2ω using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the direction.
The ratio x1 / x2 is
  • 2
  • 1/2

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  • It is ω for both the cases

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  • It is vertical for both the cases (a) and (b)
  • It is vertical for case (a); and is at 45° to the x – z plane and lies in the plane of the disc for case (b)
  • It is horizontal for case (a); and is at 45° to the x – z plane and is normal to the plane of the disc for case (b)
  • It is vertical of case (a); and is at 45° to the x – z plane and is normal to the plane of the disc for case (b)

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  • 9
  • 5
  • 4
  • 3
A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is
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  • 4
  • 3
  • 2
  • 1

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  • 8
Assertion The centre of mass of a two particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason Product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The centre of mass of system of n particles is the weighted average of the position vector of the n particles making up the system.
Reason The position of the centre of mass of a system is independent of co-ordinate system.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The centre of mass of an isolated system has a constant velocity.
Reason If centre of mass of an isolated system is already at rest, it remains at rest.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The centre of mass of a body may lie where there is no mass.
Reason Centre of mass of a body is a point, where two whole mass of the body is supposed to be concentrated.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion A particle is moving on a straight line with a uniform velocity, its angular momentum is always zero.
Reason The momentum is zero when particle moves with a uniform velocity.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The centre of mass of a proton and an electron, released from their respective positions remains at rest.
Reason The centre of mass remain at rest, if no external force is applied.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The position of centre of mass of a body does not depend upon shape and size of the body.
Reason Centre of mass of a body lies always at the centre of the body.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Out of the given bodies (of same mass) for which the moment of inertia will be maximum about the axis passing through its centre of gravity and perpendicular
  • Disc of radius a
  • Ring of radius a
  • Square lamina of side 2a
  • Four rods of length 2a making a square
Assertion A judo fighter in order to throw his opponent on to the mattries he initially bend his opponent and then rotate him around his hip.
Reason As the mass of the opponent is brought doser to the fighter\'s hip, the force required to throw the opponent is reduced.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The centre of mass of an electron and proton, when released moves faster towards proton.
Reason Proton is heavier than electron.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion At the centre of earth, a body has centre of mass, but no centre of gravity.
Reason Acceleration due to gravity is zero at the centre of earth.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction.
Reason Explosion occur under internal forces only. External force is zero.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion Moment of inertia of a particle is same, whatever be the axis of rotation.
Reason Moment of inertia depends on mass and distance of the particles.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion Inertia and moment of inertia are same quantities.
Reason Inertia represents the capacity of a body to oppose its state of motion or rest.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion If earth shrink (without change in mass) to half its present size, length of the day would become 6 hours.
Reason As size of the earth changes its moment of inertia changes.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.

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  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion Radius of gyration of a body is a constant quantity.
Reason The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particle from the axis of rotation.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion A ladder is more apt to slip, when you are high up on it than when you just begin to climb.
Reason At the high up on a ladder, the torque is large and on climbing up the torque is small.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion Torque is equal to rate of change of angular momentum.
Reason Angular momentum depends on moment of inertia and angular velocity.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The speed of whirlwind in a tornado is alarmingly high.
Reason If no external torque acts on a body, its angular velocity remains conserved.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The velocity of a body at the bottom of an inclined plane of given height, is more when is slides down the plane, compared to, when it is rolling down the same plane.
Reason In rolling down, a body aquires both, kinetic energy of translation and rotation.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion In rolling, all points of a rigid body have the same linear speed.
Reason The rotational motion does not affect the linear velocity of rigid body.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion).
Reason For perfect rolling motion, work down against friction is zero.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
Assertion The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.
Reason For all solid bodies total kinetic energy is always twice the translational kinetic energy.
  • If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
  • If Assertion is true but Reason is false.
  • If The Assertion and Reason both are false.
  • If Assertion is false but Reason is true.
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